Mixing
Find the minimal initial values
Clash Royale CLAN TAG#URR8PPP
up vote
6
down vote
favorite
Consider a sequence F of positive integers where F(n) = F(n-1) + F(n-2) for n >= 2. The Fibonacci sequence is one example of this type of sequence for F(0) = F(1) = 1, but any two initial values will yield a different sequence. For example F(0) = 3, F(1) = 1 produces these terms.
3, 1, 4, 5, 9, 14, 23, 37, 60, 97, ...
Challenge
The task is to find F(0) and F(1) that minimize F(0) + F(1) given some term of a sequence F(n). Write a function or complete program to complete the task.
Input
Input is a single positive integer, F(n). It may be accepted as a parameter or from standard input. Any reasonable representation is allowed, including direct integer or string representations.
Invalid inputs need not be considered.
Output
The output will be two positive integers, F(0) and F(1). Any reasonable format is acceptable. Here are some examples of reasonable formats.
- Written on separate lines to standard output
- Formatted on standard output as a delimited 2-element list
- Returned as a tuple or 2-element array of integers from a function
Examples
60 -> [3, 1]
37 -> [3, 1]
13 -> [1, 1]
26 -> [2, 2]
4 -> [2, 1]
5 -> [1, 1]
6 -> [2, 2]
7 -> [2, 1]
12 -> [3, 2]
1 -> [1, 1]
Scoring
This is code golf. The score is calculated by bytes of source code.
Sandbox
code-golf
asked 2 hours ago
recursive
4,8241221
add a comment |Â
up vote
6
down vote
favorite
Consider a sequence F of positive integers where F(n) = F(n-1) + F(n-2) for n >= 2. The Fibonacci sequence is one example of this type of sequence for F(0) = F(1) = 1, but any two initial values will yield a different sequence. For example F(0) = 3, F(1) = 1 produces these terms.
3, 1, 4, 5, 9, 14, 23, 37, 60, 97, ...
Challenge
The task is to find F(0) and F(1) that minimize F(0) + F(1) given some term of a sequence F(n). Write a function or complete program to complete the task.
Input
Input is a single positive integer, F(n). It may be accepted as a parameter or from standard input. Any reasonable representation is allowed, including direct integer or string representations.
Invalid inputs need not be considered.
Output
The output will be two positive integers, F(0) and F(1). Any reasonable format is acceptable. Here are some examples of reasonable formats.
- Written on separate lines to standard output
- Formatted on standard output as a delimited 2-element list
- Returned as a tuple or 2-element array of integers from a function
Examples
60 -> [3, 1]
37 -> [3, 1]
13 -> [1, 1]
26 -> [2, 2]
4 -> [2, 1]
5 -> [1, 1]
6 -> [2, 2]
7 -> [2, 1]
12 -> [3, 2]
1 -> [1, 1]
Scoring
This is code golf. The score is calculated by bytes of source code.
Sandbox
code-golf
asked 2 hours ago
recursive
4,8241221
does12 -> [4, 0]count?
– Flame
2 hours ago
Fis a sequence of positive integers, and 0 isn't positive, so that's not valid.
– recursive
2 hours ago
Nitpick: the Fibonacci sequence may be defined by $F[0] = 0, F[1] = 1$ or $F[1] = F[2] = 1$. Many of the sequence's well-known properties rely on this indexing.
– Dennis♦
16 mins ago
add a comment |Â
up vote
6
down vote
favorite
up vote
6
down vote
favorite
Consider a sequence F of positive integers where F(n) = F(n-1) + F(n-2) for n >= 2. The Fibonacci sequence is one example of this type of sequence for F(0) = F(1) = 1, but any two initial values will yield a different sequence. For example F(0) = 3, F(1) = 1 produces these terms.
3, 1, 4, 5, 9, 14, 23, 37, 60, 97, ...
Challenge
The task is to find F(0) and F(1) that minimize F(0) + F(1) given some term of a sequence F(n). Write a function or complete program to complete the task.
Input
Input is a single positive integer, F(n). It may be accepted as a parameter or from standard input. Any reasonable representation is allowed, including direct integer or string representations.
Invalid inputs need not be considered.
Output
The output will be two positive integers, F(0) and F(1). Any reasonable format is acceptable. Here are some examples of reasonable formats.
- Written on separate lines to standard output
- Formatted on standard output as a delimited 2-element list
- Returned as a tuple or 2-element array of integers from a function
Examples
60 -> [3, 1]
37 -> [3, 1]
13 -> [1, 1]
26 -> [2, 2]
4 -> [2, 1]
5 -> [1, 1]
6 -> [2, 2]
7 -> [2, 1]
12 -> [3, 2]
1 -> [1, 1]
Scoring
This is code golf. The score is calculated by bytes of source code.
Sandbox
code-golf
asked 2 hours ago
recursive
4,8241221
Consider a sequence F of positive integers where F(n) = F(n-1) + F(n-2) for n >= 2. The Fibonacci sequence is one example of this type of sequence for F(0) = F(1) = 1, but any two initial values will yield a different sequence. For example F(0) = 3, F(1) = 1 produces these terms.
3, 1, 4, 5, 9, 14, 23, 37, 60, 97, ...
Challenge
The task is to find F(0) and F(1) that minimize F(0) + F(1) given some term of a sequence F(n). Write a function or complete program to complete the task.
Input
Input is a single positive integer, F(n). It may be accepted as a parameter or from standard input. Any reasonable representation is allowed, including direct integer or string representations.
Invalid inputs need not be considered.
Output
The output will be two positive integers, F(0) and F(1). Any reasonable format is acceptable. Here are some examples of reasonable formats.
- Written on separate lines to standard output
- Formatted on standard output as a delimited 2-element list
- Returned as a tuple or 2-element array of integers from a function
Examples
60 -> [3, 1]
37 -> [3, 1]
13 -> [1, 1]
26 -> [2, 2]
4 -> [2, 1]
5 -> [1, 1]
6 -> [2, 2]
7 -> [2, 1]
12 -> [3, 2]
1 -> [1, 1]
Scoring
This is code golf. The score is calculated by bytes of source code.
Sandbox
code-golf
code-golf
asked 2 hours ago
recursive
4,8241221
asked 2 hours ago
recursive
4,8241221
edited 2 hours ago
asked 2 hours ago
recursive
4,8241221
asked 2 hours ago
recursive
4,8241221
asked 2 hours ago
recursive
4,8241221
4,8241221
does12 -> [4, 0]count?
– Flame
2 hours ago
Fis a sequence of positive integers, and 0 isn't positive, so that's not valid.
– recursive
2 hours ago
Nitpick: the Fibonacci sequence may be defined by $F[0] = 0, F[1] = 1$ or $F[1] = F[2] = 1$. Many of the sequence's well-known properties rely on this indexing.
– Dennis♦
16 mins ago
add a comment |Â
does12 -> [4, 0]count?
– Flame
2 hours ago
Fis a sequence of positive integers, and 0 isn't positive, so that's not valid.
– recursive
2 hours ago
Nitpick: the Fibonacci sequence may be defined by $F[0] = 0, F[1] = 1$ or $F[1] = F[2] = 1$. Many of the sequence's well-known properties rely on this indexing.
– Dennis♦
16 mins ago
does
12 -> [4, 0] count?– Flame
2 hours ago
does
12 -> [4, 0] count?– Flame
2 hours ago
F is a sequence of positive integers, and 0 isn't positive, so that's not valid.– recursive
2 hours ago
F is a sequence of positive integers, and 0 isn't positive, so that's not valid.– recursive
2 hours ago
Nitpick: the Fibonacci sequence may be defined by $F[0] = 0, F[1] = 1$ or $F[1] = F[2] = 1$. Many of the sequence's well-known properties rely on this indexing.
– Dennis♦
16 mins ago
Nitpick: the Fibonacci sequence may be defined by $F[0] = 0, F[1] = 1$ or $F[1] = F[2] = 1$. Many of the sequence's well-known properties rely on this indexing.
– Dennis♦
16 mins ago
add a comment |Â
5 Answers
5
active
oldest
votes
up vote
1
down vote
Japt, 34 bytes
_Ì<U?[ZÌZx]gV:ZÌ
õ ïUõ)ñx æ_gV ¥U
Try it online!
The empty first line is important.
Explanation:
_ Declare a function V:
Ì<U? :ZÌ If the second number is >= n, return it
[ZÌZx]gV Otherwise call V again with the second number and the sum
õ ïUõ) Get all pairs of positive integers where both are less than n
ñx Sort them by their sum
æ_gV ¥U Return the first (lowest sum) one where V returns n
answered 22 mins ago
Kamil Drakari
2,421416
add a comment |Â
up vote
1
down vote
Jelly, 13 bytes
pWạṚ$</¿€SÞḢ
Try it online!
How it works
pWạṚ$</¿€SÞḢ Main link. Argument: n
W Wrap; yield [n].
p Cartesian product; promote the left argument n to [1, ..., n] and take
the product of [1, ..., n] and n, yielding [[1, n], ..., [n, n]].
€ Map the link to the left over the pairs [k, n].
¿ While...
</ reducing the pair by less-than yields 1:
ạ Cumulatively reduce the pair by absolute difference.
Ṛ Reverse the result.
In essence, starting with [a, b] := [k, n], we keep executing
[a, b] := [b, |a - b|], until the pair is no longer increasing.
SÞ Sort the resulting pairs by their sums.
Ḣ Head; extract the first pair.
answered 21 mins ago
Dennis♦
183k32293726
add a comment |Â
up vote
0
down vote
JavaScript (216 characters)
function f(r)for(var n=1;;)var f=p(n);for(var u in f)if(s(f[u][0],f[u][1],r))return f[u];n++function p(r)for(var n=,f=1;0<r;)n.push([r,f]),r--,f++;return nfunction s(r,n,f)
https://jsfiddle.net/twkz2gyb/
(Ungolfed code):
// For a given input n, return all combinations of positive integers that sum to n.
function findPairs(n)
var arr = ;
var b = 1;
while(n > 0)
arr.push([n, b]);
n--;
b++;
return arr;
// Run a sequence for a and b, and continue fibonacci'ing until r is found(or quit if past r).
function sequence(a, b, r)
if(b === r)
return true;
else if(b > r)
return null;
var nextFibo = a + b;
return sequence(b, nextFibo, r);
// For a given n, find the first 2 numbers of the fibonacci sequence with the smallest sum that result in n.
function find(n)
var i = 1;
while(i < 10)
var pairs = findPairs(i);
for(var p in pairs)
var result = sequence(pairs[p][0], pairs[p][1], n);
if(result)
return pairs[p];
i++;
answered 1 hour ago
Flame
1312
add a comment |Â
up vote
0
down vote
Haskell, 81 bytes
f x=head[(a,s-a)|s<-[2..],a<-[1..s-1],let u=s-a:zipWith(+)u(a:u),x`elem`take x u]
Try it online!
answered 29 mins ago
Delfad0r
1,153315
add a comment |Â
up vote
0
down vote
Perl 6, 52 bytes
->n(1..n X 1..n).max:(n∈(
Try it online!
Brute-force solution.
answered 40 mins ago
nwellnhof
5,188920
add a comment |Â
5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Japt, 34 bytes
_Ì<U?[ZÌZx]gV:ZÌ
õ ïUõ)ñx æ_gV ¥U
Try it online!
The empty first line is important.
Explanation:
_ Declare a function V:
Ì<U? :ZÌ If the second number is >= n, return it
[ZÌZx]gV Otherwise call V again with the second number and the sum
õ ïUõ) Get all pairs of positive integers where both are less than n
ñx Sort them by their sum
æ_gV ¥U Return the first (lowest sum) one where V returns n
answered 22 mins ago
Kamil Drakari
2,421416
add a comment |Â
up vote
1
down vote
Japt, 34 bytes
_Ì<U?[ZÌZx]gV:ZÌ
õ ïUõ)ñx æ_gV ¥U
Try it online!
The empty first line is important.
Explanation:
_ Declare a function V:
Ì<U? :ZÌ If the second number is >= n, return it
[ZÌZx]gV Otherwise call V again with the second number and the sum
õ ïUõ) Get all pairs of positive integers where both are less than n
ñx Sort them by their sum
æ_gV ¥U Return the first (lowest sum) one where V returns n
answered 22 mins ago
Kamil Drakari
2,421416
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Japt, 34 bytes
_Ì<U?[ZÌZx]gV:ZÌ
õ ïUõ)ñx æ_gV ¥U
Try it online!
The empty first line is important.
Explanation:
_ Declare a function V:
Ì<U? :ZÌ If the second number is >= n, return it
[ZÌZx]gV Otherwise call V again with the second number and the sum
õ ïUõ) Get all pairs of positive integers where both are less than n
ñx Sort them by their sum
æ_gV ¥U Return the first (lowest sum) one where V returns n
answered 22 mins ago
Kamil Drakari
2,421416
Japt, 34 bytes
_Ì<U?[ZÌZx]gV:ZÌ
õ ïUõ)ñx æ_gV ¥U
Try it online!
The empty first line is important.
Explanation:
_ Declare a function V:
Ì<U? :ZÌ If the second number is >= n, return it
[ZÌZx]gV Otherwise call V again with the second number and the sum
õ ïUõ) Get all pairs of positive integers where both are less than n
ñx Sort them by their sum
æ_gV ¥U Return the first (lowest sum) one where V returns n
answered 22 mins ago
Kamil Drakari
2,421416
answered 22 mins ago
Kamil Drakari
2,421416
answered 22 mins ago
Kamil Drakari
2,421416
answered 22 mins ago
Kamil Drakari
2,421416
2,421416
add a comment |Â
add a comment |Â
up vote
1
down vote
Jelly, 13 bytes
pWạṚ$</¿€SÞḢ
Try it online!
How it works
pWạṚ$</¿€SÞḢ Main link. Argument: n
W Wrap; yield [n].
p Cartesian product; promote the left argument n to [1, ..., n] and take
the product of [1, ..., n] and n, yielding [[1, n], ..., [n, n]].
€ Map the link to the left over the pairs [k, n].
¿ While...
</ reducing the pair by less-than yields 1:
ạ Cumulatively reduce the pair by absolute difference.
Ṛ Reverse the result.
In essence, starting with [a, b] := [k, n], we keep executing
[a, b] := [b, |a - b|], until the pair is no longer increasing.
SÞ Sort the resulting pairs by their sums.
Ḣ Head; extract the first pair.
answered 21 mins ago
Dennis♦
183k32293726
add a comment |Â
up vote
1
down vote
Jelly, 13 bytes
pWạṚ$</¿€SÞḢ
Try it online!
How it works
pWạṚ$</¿€SÞḢ Main link. Argument: n
W Wrap; yield [n].
p Cartesian product; promote the left argument n to [1, ..., n] and take
the product of [1, ..., n] and n, yielding [[1, n], ..., [n, n]].
€ Map the link to the left over the pairs [k, n].
¿ While...
</ reducing the pair by less-than yields 1:
ạ Cumulatively reduce the pair by absolute difference.
Ṛ Reverse the result.
In essence, starting with [a, b] := [k, n], we keep executing
[a, b] := [b, |a - b|], until the pair is no longer increasing.
SÞ Sort the resulting pairs by their sums.
Ḣ Head; extract the first pair.
answered 21 mins ago
Dennis♦
183k32293726
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Jelly, 13 bytes
pWạṚ$</¿€SÞḢ
Try it online!
How it works
pWạṚ$</¿€SÞḢ Main link. Argument: n
W Wrap; yield [n].
p Cartesian product; promote the left argument n to [1, ..., n] and take
the product of [1, ..., n] and n, yielding [[1, n], ..., [n, n]].
€ Map the link to the left over the pairs [k, n].
¿ While...
</ reducing the pair by less-than yields 1:
ạ Cumulatively reduce the pair by absolute difference.
Ṛ Reverse the result.
In essence, starting with [a, b] := [k, n], we keep executing
[a, b] := [b, |a - b|], until the pair is no longer increasing.
SÞ Sort the resulting pairs by their sums.
Ḣ Head; extract the first pair.
answered 21 mins ago
Dennis♦
183k32293726
Jelly, 13 bytes
pWạṚ$</¿€SÞḢ
Try it online!
How it works
pWạṚ$</¿€SÞḢ Main link. Argument: n
W Wrap; yield [n].
p Cartesian product; promote the left argument n to [1, ..., n] and take
the product of [1, ..., n] and n, yielding [[1, n], ..., [n, n]].
€ Map the link to the left over the pairs [k, n].
¿ While...
</ reducing the pair by less-than yields 1:
ạ Cumulatively reduce the pair by absolute difference.
Ṛ Reverse the result.
In essence, starting with [a, b] := [k, n], we keep executing
[a, b] := [b, |a - b|], until the pair is no longer increasing.
SÞ Sort the resulting pairs by their sums.
Ḣ Head; extract the first pair.
answered 21 mins ago
Dennis♦
183k32293726
edited 8 mins ago
answered 21 mins ago
Dennis♦
183k32293726
answered 21 mins ago
Dennis♦
183k32293726
answered 21 mins ago
Dennis♦
183k32293726
183k32293726
add a comment |Â
add a comment |Â
up vote
0
down vote
JavaScript (216 characters)
function f(r)for(var n=1;;)var f=p(n);for(var u in f)if(s(f[u][0],f[u][1],r))return f[u];n++function p(r)for(var n=,f=1;0<r;)n.push([r,f]),r--,f++;return nfunction s(r,n,f)
https://jsfiddle.net/twkz2gyb/
(Ungolfed code):
// For a given input n, return all combinations of positive integers that sum to n.
function findPairs(n)
var arr = ;
var b = 1;
while(n > 0)
arr.push([n, b]);
n--;
b++;
return arr;
// Run a sequence for a and b, and continue fibonacci'ing until r is found(or quit if past r).
function sequence(a, b, r)
if(b === r)
return true;
else if(b > r)
return null;
var nextFibo = a + b;
return sequence(b, nextFibo, r);
// For a given n, find the first 2 numbers of the fibonacci sequence with the smallest sum that result in n.
function find(n)
var i = 1;
while(i < 10)
var pairs = findPairs(i);
for(var p in pairs)
var result = sequence(pairs[p][0], pairs[p][1], n);
if(result)
return pairs[p];
i++;
answered 1 hour ago
Flame
1312
add a comment |Â
up vote
0
down vote
JavaScript (216 characters)
function f(r)for(var n=1;;)var f=p(n);for(var u in f)if(s(f[u][0],f[u][1],r))return f[u];n++function p(r)for(var n=,f=1;0<r;)n.push([r,f]),r--,f++;return nfunction s(r,n,f)
https://jsfiddle.net/twkz2gyb/
(Ungolfed code):
// For a given input n, return all combinations of positive integers that sum to n.
function findPairs(n)
var arr = ;
var b = 1;
while(n > 0)
arr.push([n, b]);
n--;
b++;
return arr;
// Run a sequence for a and b, and continue fibonacci'ing until r is found(or quit if past r).
function sequence(a, b, r)
if(b === r)
return true;
else if(b > r)
return null;
var nextFibo = a + b;
return sequence(b, nextFibo, r);
// For a given n, find the first 2 numbers of the fibonacci sequence with the smallest sum that result in n.
function find(n)
var i = 1;
while(i < 10)
var pairs = findPairs(i);
for(var p in pairs)
var result = sequence(pairs[p][0], pairs[p][1], n);
if(result)
return pairs[p];
i++;
answered 1 hour ago
Flame
1312
add a comment |Â
up vote
0
down vote
up vote
0
down vote
JavaScript (216 characters)
function f(r)for(var n=1;;)var f=p(n);for(var u in f)if(s(f[u][0],f[u][1],r))return f[u];n++function p(r)for(var n=,f=1;0<r;)n.push([r,f]),r--,f++;return nfunction s(r,n,f)
https://jsfiddle.net/twkz2gyb/
(Ungolfed code):
// For a given input n, return all combinations of positive integers that sum to n.
function findPairs(n)
var arr = ;
var b = 1;
while(n > 0)
arr.push([n, b]);
n--;
b++;
return arr;
// Run a sequence for a and b, and continue fibonacci'ing until r is found(or quit if past r).
function sequence(a, b, r)
if(b === r)
return true;
else if(b > r)
return null;
var nextFibo = a + b;
return sequence(b, nextFibo, r);
// For a given n, find the first 2 numbers of the fibonacci sequence with the smallest sum that result in n.
function find(n)
var i = 1;
while(i < 10)
var pairs = findPairs(i);
for(var p in pairs)
var result = sequence(pairs[p][0], pairs[p][1], n);
if(result)
return pairs[p];
i++;
answered 1 hour ago
Flame
1312
JavaScript (216 characters)
function f(r)for(var n=1;;)var f=p(n);for(var u in f)if(s(f[u][0],f[u][1],r))return f[u];n++function p(r)for(var n=,f=1;0<r;)n.push([r,f]),r--,f++;return nfunction s(r,n,f)
https://jsfiddle.net/twkz2gyb/
(Ungolfed code):
// For a given input n, return all combinations of positive integers that sum to n.
function findPairs(n)
var arr = ;
var b = 1;
while(n > 0)
arr.push([n, b]);
n--;
b++;
return arr;
// Run a sequence for a and b, and continue fibonacci'ing until r is found(or quit if past r).
function sequence(a, b, r)
if(b === r)
return true;
else if(b > r)
return null;
var nextFibo = a + b;
return sequence(b, nextFibo, r);
// For a given n, find the first 2 numbers of the fibonacci sequence with the smallest sum that result in n.
function find(n)
var i = 1;
while(i < 10)
var pairs = findPairs(i);
for(var p in pairs)
var result = sequence(pairs[p][0], pairs[p][1], n);
if(result)
return pairs[p];
i++;
answered 1 hour ago
Flame
1312
answered 1 hour ago
Flame
1312
answered 1 hour ago
Flame
1312
answered 1 hour ago
Flame
1312
1312
add a comment |Â
add a comment |Â
up vote
0
down vote
Haskell, 81 bytes
f x=head[(a,s-a)|s<-[2..],a<-[1..s-1],let u=s-a:zipWith(+)u(a:u),x`elem`take x u]
Try it online!
answered 29 mins ago
Delfad0r
1,153315
add a comment |Â
up vote
0
down vote
Haskell, 81 bytes
f x=head[(a,s-a)|s<-[2..],a<-[1..s-1],let u=s-a:zipWith(+)u(a:u),x`elem`take x u]
Try it online!
answered 29 mins ago
Delfad0r
1,153315
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Haskell, 81 bytes
f x=head[(a,s-a)|s<-[2..],a<-[1..s-1],let u=s-a:zipWith(+)u(a:u),x`elem`take x u]
Try it online!
answered 29 mins ago
Delfad0r
1,153315
Haskell, 81 bytes
f x=head[(a,s-a)|s<-[2..],a<-[1..s-1],let u=s-a:zipWith(+)u(a:u),x`elem`take x u]
Try it online!
answered 29 mins ago
Delfad0r
1,153315
answered 29 mins ago
Delfad0r
1,153315
answered 29 mins ago
Delfad0r
1,153315
answered 29 mins ago
Delfad0r
1,153315
1,153315
add a comment |Â
add a comment |Â
up vote
0
down vote
Perl 6, 52 bytes
->n(1..n X 1..n).max:(n∈(
Try it online!
Brute-force solution.
answered 40 mins ago
nwellnhof
5,188920
add a comment |Â
up vote
0
down vote
Perl 6, 52 bytes
->n(1..n X 1..n).max:(n∈(
Try it online!
Brute-force solution.
answered 40 mins ago
nwellnhof
5,188920
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Perl 6, 52 bytes
->n(1..n X 1..n).max:(n∈(
Try it online!
Brute-force solution.
answered 40 mins ago
nwellnhof
5,188920
Perl 6, 52 bytes
->n(1..n X 1..n).max:(n∈(
Try it online!
Brute-force solution.
answered 40 mins ago
nwellnhof
5,188920
edited 2 mins ago
answered 40 mins ago
nwellnhof
5,188920
answered 40 mins ago
nwellnhof
5,188920
answered 40 mins ago
nwellnhof
5,188920
5,188920
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodegolf.stackexchange.com%2fquestions%2f175118%2ffind-the-minimal-initial-values%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
does
12 -> [4, 0]count?– Flame
2 hours ago
Fis a sequence of positive integers, and 0 isn't positive, so that's not valid.– recursive
2 hours ago
Nitpick: the Fibonacci sequence may be defined by $F[0] = 0, F[1] = 1$ or $F[1] = F[2] = 1$. Many of the sequence's well-known properties rely on this indexing.
– Dennis♦
16 mins ago