Mixing
New Neighbour Sequence
Clash Royale CLAN TAG#URR8PPP
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The non-negative integers are bored of always having the same two* neighbours, so they decide to mix things up a little. However, they are also lazy and want to stay as close as possible to their original position.
They come up with the following algorithm:
- The first element is 0.
- The $n^th$ element is the smallest number which is not yet present in the sequence and which is not a neighbour of the $(n-1)^th$ element.
This generates the following infinite sequence:
0,2,4,1,3,5,7,9,6,8,10,12,14,11,13,15,17,19,16,18,20,22,24,21,23,25,27,29,26,28 ...
0 is the first element. 1 is the smallest number not yet in the sequence, but it is a neighbour of 0. The next smallest number is 2, so it is the second element of the sequence. Now the remaining numbers are 1,3,4,5,6,..., but as both 1 and 3 are neighbours of 2, 4 is the third member of the sequence. As 1 is not a neighbour of 4, it can finally take its place as fourth element.
The Task
Write a function or program in as few bytes as possible which generates the above sequence.
You may
- output the sequence infinitely,
- take an input $n$ and return the $n^th$ element of the sequence, or
- take an input $n$ and return the first $n$ elements of the sequence.
Both zero- or one-indexing is fine in case you choose one of the two later options.
You don't need to follow the algorithm given above, any method which produces the same sequence is fine.
Inspired by Code golf the best permutation. Turns out this is A277618.
* Zero has literally only one neighbour and doesn't really care.
code-golf sequence integer
asked 1 hour ago
Laikoni
19.1k43594
add a comment |Â
up vote
5
down vote
favorite
The non-negative integers are bored of always having the same two* neighbours, so they decide to mix things up a little. However, they are also lazy and want to stay as close as possible to their original position.
They come up with the following algorithm:
- The first element is 0.
- The $n^th$ element is the smallest number which is not yet present in the sequence and which is not a neighbour of the $(n-1)^th$ element.
This generates the following infinite sequence:
0,2,4,1,3,5,7,9,6,8,10,12,14,11,13,15,17,19,16,18,20,22,24,21,23,25,27,29,26,28 ...
0 is the first element. 1 is the smallest number not yet in the sequence, but it is a neighbour of 0. The next smallest number is 2, so it is the second element of the sequence. Now the remaining numbers are 1,3,4,5,6,..., but as both 1 and 3 are neighbours of 2, 4 is the third member of the sequence. As 1 is not a neighbour of 4, it can finally take its place as fourth element.
The Task
Write a function or program in as few bytes as possible which generates the above sequence.
You may
- output the sequence infinitely,
- take an input $n$ and return the $n^th$ element of the sequence, or
- take an input $n$ and return the first $n$ elements of the sequence.
Both zero- or one-indexing is fine in case you choose one of the two later options.
You don't need to follow the algorithm given above, any method which produces the same sequence is fine.
Inspired by Code golf the best permutation. Turns out this is A277618.
* Zero has literally only one neighbour and doesn't really care.
code-golf sequence integer
asked 1 hour ago
Laikoni
19.1k43594
Sandbox post (deleted)
– Laikoni
1 hour ago
add a comment |Â
up vote
5
down vote
favorite
up vote
5
down vote
favorite
The non-negative integers are bored of always having the same two* neighbours, so they decide to mix things up a little. However, they are also lazy and want to stay as close as possible to their original position.
They come up with the following algorithm:
- The first element is 0.
- The $n^th$ element is the smallest number which is not yet present in the sequence and which is not a neighbour of the $(n-1)^th$ element.
This generates the following infinite sequence:
0,2,4,1,3,5,7,9,6,8,10,12,14,11,13,15,17,19,16,18,20,22,24,21,23,25,27,29,26,28 ...
0 is the first element. 1 is the smallest number not yet in the sequence, but it is a neighbour of 0. The next smallest number is 2, so it is the second element of the sequence. Now the remaining numbers are 1,3,4,5,6,..., but as both 1 and 3 are neighbours of 2, 4 is the third member of the sequence. As 1 is not a neighbour of 4, it can finally take its place as fourth element.
The Task
Write a function or program in as few bytes as possible which generates the above sequence.
You may
- output the sequence infinitely,
- take an input $n$ and return the $n^th$ element of the sequence, or
- take an input $n$ and return the first $n$ elements of the sequence.
Both zero- or one-indexing is fine in case you choose one of the two later options.
You don't need to follow the algorithm given above, any method which produces the same sequence is fine.
Inspired by Code golf the best permutation. Turns out this is A277618.
* Zero has literally only one neighbour and doesn't really care.
code-golf sequence integer
asked 1 hour ago
Laikoni
19.1k43594
The non-negative integers are bored of always having the same two* neighbours, so they decide to mix things up a little. However, they are also lazy and want to stay as close as possible to their original position.
They come up with the following algorithm:
- The first element is 0.
- The $n^th$ element is the smallest number which is not yet present in the sequence and which is not a neighbour of the $(n-1)^th$ element.
This generates the following infinite sequence:
0,2,4,1,3,5,7,9,6,8,10,12,14,11,13,15,17,19,16,18,20,22,24,21,23,25,27,29,26,28 ...
0 is the first element. 1 is the smallest number not yet in the sequence, but it is a neighbour of 0. The next smallest number is 2, so it is the second element of the sequence. Now the remaining numbers are 1,3,4,5,6,..., but as both 1 and 3 are neighbours of 2, 4 is the third member of the sequence. As 1 is not a neighbour of 4, it can finally take its place as fourth element.
The Task
Write a function or program in as few bytes as possible which generates the above sequence.
You may
- output the sequence infinitely,
- take an input $n$ and return the $n^th$ element of the sequence, or
- take an input $n$ and return the first $n$ elements of the sequence.
Both zero- or one-indexing is fine in case you choose one of the two later options.
You don't need to follow the algorithm given above, any method which produces the same sequence is fine.
Inspired by Code golf the best permutation. Turns out this is A277618.
* Zero has literally only one neighbour and doesn't really care.
code-golf sequence integer
code-golf sequence integer
asked 1 hour ago
Laikoni
19.1k43594
asked 1 hour ago
Laikoni
19.1k43594
asked 1 hour ago
Laikoni
19.1k43594
asked 1 hour ago
Laikoni
19.1k43594
asked 1 hour ago
Laikoni
19.1k43594
19.1k43594
Sandbox post (deleted)
– Laikoni
1 hour ago
add a comment |Â
Sandbox post (deleted)
– Laikoni
1 hour ago
Sandbox post (deleted)
– Laikoni
1 hour ago
Sandbox post (deleted)
– Laikoni
1 hour ago
add a comment |Â
4 Answers
4
active
oldest
votes
up vote
2
down vote
Python 2, 20 bytes
lambda n:2*n%5+n/5*5
Try it online!
answered 1 hour ago
Chas Brown
4,5061419
add a comment |Â
up vote
1
down vote
JavaScript (ES6), 13 bytes
Returns the $n$th term of the sequence.
n=>n-2-~++n%5
Try it online!
answered 35 mins ago
Arnauld
66.8k584281
add a comment |Â
up vote
0
down vote
Wolfram Language (Mathematica), 14 bytes
#+Mod[#,5,-2]&
Try it online!
Prints the n-th, zero-indexed, integer in the sequence.
answered 1 hour ago
Misha Lavrov
3,617320
add a comment |Â
up vote
0
down vote
Common Lisp, 67 bytes
(defun x(n)(loop for a from 0 to n collect(+(mod(+ a 2)5)(- a 2))))
Try it online!
answered 13 mins ago
JRowan
1814
add a comment |Â
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Python 2, 20 bytes
lambda n:2*n%5+n/5*5
Try it online!
answered 1 hour ago
Chas Brown
4,5061419
add a comment |Â
up vote
2
down vote
Python 2, 20 bytes
lambda n:2*n%5+n/5*5
Try it online!
answered 1 hour ago
Chas Brown
4,5061419
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Python 2, 20 bytes
lambda n:2*n%5+n/5*5
Try it online!
answered 1 hour ago
Chas Brown
4,5061419
Python 2, 20 bytes
lambda n:2*n%5+n/5*5
Try it online!
answered 1 hour ago
Chas Brown
4,5061419
answered 1 hour ago
Chas Brown
4,5061419
answered 1 hour ago
Chas Brown
4,5061419
answered 1 hour ago
Chas Brown
4,5061419
4,5061419
add a comment |Â
add a comment |Â
up vote
1
down vote
JavaScript (ES6), 13 bytes
Returns the $n$th term of the sequence.
n=>n-2-~++n%5
Try it online!
answered 35 mins ago
Arnauld
66.8k584281
add a comment |Â
up vote
1
down vote
JavaScript (ES6), 13 bytes
Returns the $n$th term of the sequence.
n=>n-2-~++n%5
Try it online!
answered 35 mins ago
Arnauld
66.8k584281
add a comment |Â
up vote
1
down vote
up vote
1
down vote
JavaScript (ES6), 13 bytes
Returns the $n$th term of the sequence.
n=>n-2-~++n%5
Try it online!
answered 35 mins ago
Arnauld
66.8k584281
JavaScript (ES6), 13 bytes
Returns the $n$th term of the sequence.
n=>n-2-~++n%5
Try it online!
answered 35 mins ago
Arnauld
66.8k584281
edited 23 mins ago
answered 35 mins ago
Arnauld
66.8k584281
answered 35 mins ago
Arnauld
66.8k584281
answered 35 mins ago
Arnauld
66.8k584281
66.8k584281
add a comment |Â
add a comment |Â
up vote
0
down vote
Wolfram Language (Mathematica), 14 bytes
#+Mod[#,5,-2]&
Try it online!
Prints the n-th, zero-indexed, integer in the sequence.
answered 1 hour ago
Misha Lavrov
3,617320
add a comment |Â
up vote
0
down vote
Wolfram Language (Mathematica), 14 bytes
#+Mod[#,5,-2]&
Try it online!
Prints the n-th, zero-indexed, integer in the sequence.
answered 1 hour ago
Misha Lavrov
3,617320
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Wolfram Language (Mathematica), 14 bytes
#+Mod[#,5,-2]&
Try it online!
Prints the n-th, zero-indexed, integer in the sequence.
answered 1 hour ago
Misha Lavrov
3,617320
Wolfram Language (Mathematica), 14 bytes
#+Mod[#,5,-2]&
Try it online!
Prints the n-th, zero-indexed, integer in the sequence.
answered 1 hour ago
Misha Lavrov
3,617320
answered 1 hour ago
Misha Lavrov
3,617320
answered 1 hour ago
Misha Lavrov
3,617320
answered 1 hour ago
Misha Lavrov
3,617320
3,617320
add a comment |Â
add a comment |Â
up vote
0
down vote
Common Lisp, 67 bytes
(defun x(n)(loop for a from 0 to n collect(+(mod(+ a 2)5)(- a 2))))
Try it online!
answered 13 mins ago
JRowan
1814
add a comment |Â
up vote
0
down vote
Common Lisp, 67 bytes
(defun x(n)(loop for a from 0 to n collect(+(mod(+ a 2)5)(- a 2))))
Try it online!
answered 13 mins ago
JRowan
1814
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Common Lisp, 67 bytes
(defun x(n)(loop for a from 0 to n collect(+(mod(+ a 2)5)(- a 2))))
Try it online!
answered 13 mins ago
JRowan
1814
Common Lisp, 67 bytes
(defun x(n)(loop for a from 0 to n collect(+(mod(+ a 2)5)(- a 2))))
Try it online!
answered 13 mins ago
JRowan
1814
answered 13 mins ago
JRowan
1814
answered 13 mins ago
JRowan
1814
answered 13 mins ago
JRowan
1814
1814
add a comment |Â
add a comment |Â
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