The Written Digits Sequence

Clash Royale CLAN TAG#URR8PPP

up vote
5
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Here's a reasonably trivial sequence which is not in the Online Encyclopedia of Integer Sequences.

Start with an empty sequence then define each term as the number of characters required to write out, in English, all of the digits of the sequence so far without spaces.*

For reference the number of characters of all of the (base ten) digits in English are:

zero one two three four five six seven eight nine
4 3 3 5 4 4 3 5 5 4

(Which is the start of both A52360 and A5589.)

This makes the first entry $a(0) = 0$ since there are zero digits present in the empty sequence.

This makes the second entry $a(1) = 4$ as it takes four characters to write "zero", the only digit present so far.

This makes the third entry $a(2) = 8$ as it takes four more characters to write the "four" for a total of eight to write "zerofour".

This makes the fourth entry $a(3) = 13$ as it takes five more characters to write "eight" for a total of thirteen to write "zerofoureight".

This makes the fifth entry $a(4) = 21$ as it takes eight more characters to write "onethree" for a total of twenty-one to write "zerofoureightonethree".

...and so on. Here are the first 100 entries:

0, 4, 8, 13, 21, 27, 35, 44, 52, 59, 67, 75, 84, 93, 102, 112, 121, 130, 142, 152, 162, 171, 182, 193, 205, 216, 225, 235, 247, 259, 270, 282, 293, 305, 318, 331, 344, 357, 371, 384, 398, 412, 422, 432, 444, 456, 467, 479, 492, 503, 516, 526, 536, 548, 561, 571, 583, 597, 610, 620, 630, 642, 652, 662, 671, 682, 693, 705, 718, 731, 744, 757, 771, 784, 798, 812, 823, 836, 849, 862, 873, 888, 903, 916, 926, 936, 948, 961, 971, 983, 997, 1010, 1024, 1038, 1055, 1070, 1086, 1101, 1114, 1127

_{* We could define it for other languages and/or other bases or with spaces of course}

The challenge

Given $n$ output, in as few bytes of code as possible, any of:

• The first $n$ terms of the sequence (should work for non-negative integers)


• The value of $a(n)$ (should work for non-negative integers)


• The $n$^th term of the sequence (should work for positive integers - i.e. value of $a(n-1)$)

---

This is code-golf so the shortest answer in bytes wins for each language, and the shortest answer in bytes wins. Don't let golfing languages stop you from entering in your favourite language be it a practical one or an esoteric one!

code-golf sequence arithmetic integer

share|improve this question

asked 2 hours ago

Jonathan Allan

49.3k534161

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By the first option, do you mean that 1) 1 should output [0] and 0 should output or 2) 0 should output [0] (as in my former answer)?
  – Erik the Outgolfer
  1 hour ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @EriktheOutgolfer I mean (1) as it should return the first n terms. That is, the options are "output the sequence up to but not including a(n)", "output a(n)", or "output a(n-1)".
  – Jonathan Allan
  1 hour ago
  
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

Here's a reasonably trivial sequence which is not in the Online Encyclopedia of Integer Sequences.

Start with an empty sequence then define each term as the number of characters required to write out, in English, all of the digits of the sequence so far without spaces.*

For reference the number of characters of all of the (base ten) digits in English are:

zero one two three four five six seven eight nine
4 3 3 5 4 4 3 5 5 4

(Which is the start of both A52360 and A5589.)

This makes the first entry $a(0) = 0$ since there are zero digits present in the empty sequence.

This makes the second entry $a(1) = 4$ as it takes four characters to write "zero", the only digit present so far.

This makes the third entry $a(2) = 8$ as it takes four more characters to write the "four" for a total of eight to write "zerofour".

This makes the fourth entry $a(3) = 13$ as it takes five more characters to write "eight" for a total of thirteen to write "zerofoureight".

This makes the fifth entry $a(4) = 21$ as it takes eight more characters to write "onethree" for a total of twenty-one to write "zerofoureightonethree".

...and so on. Here are the first 100 entries:

0, 4, 8, 13, 21, 27, 35, 44, 52, 59, 67, 75, 84, 93, 102, 112, 121, 130, 142, 152, 162, 171, 182, 193, 205, 216, 225, 235, 247, 259, 270, 282, 293, 305, 318, 331, 344, 357, 371, 384, 398, 412, 422, 432, 444, 456, 467, 479, 492, 503, 516, 526, 536, 548, 561, 571, 583, 597, 610, 620, 630, 642, 652, 662, 671, 682, 693, 705, 718, 731, 744, 757, 771, 784, 798, 812, 823, 836, 849, 862, 873, 888, 903, 916, 926, 936, 948, 961, 971, 983, 997, 1010, 1024, 1038, 1055, 1070, 1086, 1101, 1114, 1127

_{* We could define it for other languages and/or other bases or with spaces of course}

The challenge

Given $n$ output, in as few bytes of code as possible, any of:

• The first $n$ terms of the sequence (should work for non-negative integers)


• The value of $a(n)$ (should work for non-negative integers)


• The $n$^th term of the sequence (should work for positive integers - i.e. value of $a(n-1)$)

---

This is code-golf so the shortest answer in bytes wins for each language, and the shortest answer in bytes wins. Don't let golfing languages stop you from entering in your favourite language be it a practical one or an esoteric one!

code-golf sequence arithmetic integer

share|improve this question

asked 2 hours ago

Jonathan Allan

49.3k534161

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By the first option, do you mean that 1) 1 should output [0] and 0 should output or 2) 0 should output [0] (as in my former answer)?
  – Erik the Outgolfer
  1 hour ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @EriktheOutgolfer I mean (1) as it should return the first n terms. That is, the options are "output the sequence up to but not including a(n)", "output a(n)", or "output a(n-1)".
  – Jonathan Allan
  1 hour ago
  
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

up vote
5
down vote

favorite

Here's a reasonably trivial sequence which is not in the Online Encyclopedia of Integer Sequences.

Start with an empty sequence then define each term as the number of characters required to write out, in English, all of the digits of the sequence so far without spaces.*

For reference the number of characters of all of the (base ten) digits in English are:

zero one two three four five six seven eight nine
4 3 3 5 4 4 3 5 5 4

(Which is the start of both A52360 and A5589.)

This makes the first entry $a(0) = 0$ since there are zero digits present in the empty sequence.

This makes the second entry $a(1) = 4$ as it takes four characters to write "zero", the only digit present so far.

This makes the third entry $a(2) = 8$ as it takes four more characters to write the "four" for a total of eight to write "zerofour".

This makes the fourth entry $a(3) = 13$ as it takes five more characters to write "eight" for a total of thirteen to write "zerofoureight".

This makes the fifth entry $a(4) = 21$ as it takes eight more characters to write "onethree" for a total of twenty-one to write "zerofoureightonethree".

...and so on. Here are the first 100 entries:

0, 4, 8, 13, 21, 27, 35, 44, 52, 59, 67, 75, 84, 93, 102, 112, 121, 130, 142, 152, 162, 171, 182, 193, 205, 216, 225, 235, 247, 259, 270, 282, 293, 305, 318, 331, 344, 357, 371, 384, 398, 412, 422, 432, 444, 456, 467, 479, 492, 503, 516, 526, 536, 548, 561, 571, 583, 597, 610, 620, 630, 642, 652, 662, 671, 682, 693, 705, 718, 731, 744, 757, 771, 784, 798, 812, 823, 836, 849, 862, 873, 888, 903, 916, 926, 936, 948, 961, 971, 983, 997, 1010, 1024, 1038, 1055, 1070, 1086, 1101, 1114, 1127

_{* We could define it for other languages and/or other bases or with spaces of course}

The challenge

Given $n$ output, in as few bytes of code as possible, any of:

• The first $n$ terms of the sequence (should work for non-negative integers)


• The value of $a(n)$ (should work for non-negative integers)


• The $n$^th term of the sequence (should work for positive integers - i.e. value of $a(n-1)$)

---

This is code-golf so the shortest answer in bytes wins for each language, and the shortest answer in bytes wins. Don't let golfing languages stop you from entering in your favourite language be it a practical one or an esoteric one!

code-golf sequence arithmetic integer

share|improve this question

asked 2 hours ago

Jonathan Allan

49.3k534161

Here's a reasonably trivial sequence which is not in the Online Encyclopedia of Integer Sequences.

Start with an empty sequence then define each term as the number of characters required to write out, in English, all of the digits of the sequence so far without spaces.*

For reference the number of characters of all of the (base ten) digits in English are:

zero one two three four five six seven eight nine
4 3 3 5 4 4 3 5 5 4

(Which is the start of both A52360 and A5589.)

This makes the first entry $a(0) = 0$ since there are zero digits present in the empty sequence.

This makes the second entry $a(1) = 4$ as it takes four characters to write "zero", the only digit present so far.

This makes the third entry $a(2) = 8$ as it takes four more characters to write the "four" for a total of eight to write "zerofour".

This makes the fourth entry $a(3) = 13$ as it takes five more characters to write "eight" for a total of thirteen to write "zerofoureight".

This makes the fifth entry $a(4) = 21$ as it takes eight more characters to write "onethree" for a total of twenty-one to write "zerofoureightonethree".

...and so on. Here are the first 100 entries:

0, 4, 8, 13, 21, 27, 35, 44, 52, 59, 67, 75, 84, 93, 102, 112, 121, 130, 142, 152, 162, 171, 182, 193, 205, 216, 225, 235, 247, 259, 270, 282, 293, 305, 318, 331, 344, 357, 371, 384, 398, 412, 422, 432, 444, 456, 467, 479, 492, 503, 516, 526, 536, 548, 561, 571, 583, 597, 610, 620, 630, 642, 652, 662, 671, 682, 693, 705, 718, 731, 744, 757, 771, 784, 798, 812, 823, 836, 849, 862, 873, 888, 903, 916, 926, 936, 948, 961, 971, 983, 997, 1010, 1024, 1038, 1055, 1070, 1086, 1101, 1114, 1127

_{* We could define it for other languages and/or other bases or with spaces of course}

The challenge

Given $n$ output, in as few bytes of code as possible, any of:

• The first $n$ terms of the sequence (should work for non-negative integers)


• The value of $a(n)$ (should work for non-negative integers)


• The $n$^th term of the sequence (should work for positive integers - i.e. value of $a(n-1)$)

---

This is code-golf so the shortest answer in bytes wins for each language, and the shortest answer in bytes wins. Don't let golfing languages stop you from entering in your favourite language be it a practical one or an esoteric one!

code-golf sequence arithmetic integer

code-golf sequence arithmetic integer

share|improve this question

asked 2 hours ago

Jonathan Allan

49.3k534161

share|improve this question

asked 2 hours ago

Jonathan Allan

49.3k534161

share|improve this question

share|improve this question

asked 2 hours ago

Jonathan Allan

49.3k534161

asked 2 hours ago

Jonathan Allan

49.3k534161

asked 2 hours ago

Jonathan Allan

49.3k534161

49.3k534161

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By the first option, do you mean that 1) 1 should output [0] and 0 should output or 2) 0 should output [0] (as in my former answer)?
  – Erik the Outgolfer
  1 hour ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @EriktheOutgolfer I mean (1) as it should return the first n terms. That is, the options are "output the sequence up to but not including a(n)", "output a(n)", or "output a(n-1)".
  – Jonathan Allan
  1 hour ago
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By the first option, do you mean that 1) 1 should output [0] and 0 should output or 2) 0 should output [0] (as in my former answer)?
  – Erik the Outgolfer
  1 hour ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @EriktheOutgolfer I mean (1) as it should return the first n terms. That is, the options are "output the sequence up to but not including a(n)", "output a(n)", or "output a(n-1)".
  – Jonathan Allan
  1 hour ago
  
  

  
  
  
  

By the first option, do you mean that 1) 1 should output [0] and 0 should output or 2) 0 should output [0] (as in my former answer)?
– Erik the Outgolfer
1 hour ago

By the first option, do you mean that 1) 1 should output [0] and 0 should output or 2) 0 should output [0] (as in my former answer)?
– Erik the Outgolfer
1 hour ago

@EriktheOutgolfer I mean (1) as it should return the first n terms. That is, the options are "output the sequence up to but not including a(n)", "output a(n)", or "output a(n-1)".
– Jonathan Allan
1 hour ago

@EriktheOutgolfer I mean (1) as it should return the first n terms. That is, the options are "output the sequence up to but not including a(n)", "output a(n)", or "output a(n-1)".
– Jonathan Allan
1 hour ago

add a comment | 

4 Answers
4

active

oldest

votes

up vote
2
down vote

Pip, 21 bytes

Lai+:$+4335443554@^Pi

Takes input $n$ as a command-line argument and outputs the first $n$ terms. Try it online!

Explanation

Lai+:$+4335443554@^Pi
 a is 1st cmdline arg; i is 0 (implicit)
La Loop (a) times:
 Pi Print i
 ^ Split it into a list of characters (i.e. digits)
 4335443554@ Use each digit to index into this number, giving the length of the
 name of the digit (0 -> 4, 1 -> 3, etc.)
 $+ Sum the results
 i+: Increment i by that amount

share|improve this answer

answered 35 mins ago

DLosc

18.5k33588

add a comment | 

up vote
1
down vote

JavaScript (Node.js), 82 bytes

f=(a,b=1,s=4)=>a?b<a?f(a,++b,s+=[...s+''].reduce((q,w)=>+'4335443554'[w]+q,0)):s:0

Try it online!

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

add a comment | 

up vote
1
down vote

Jelly, 13 bytes

ṃ“vẋç’ḃ5¤S+Ɗ¡

Try it online!

0-indexed.

Full program; takes input from STDIN.

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Erik the Outgolfer

29.8k42899

add a comment | 

up vote
0
down vote

05AB1E, 15 bytes

ÎFD•16|/•sSèOO

Try it online!

Explanation

Î # initialize stack with 0 and input
 F # input times do:
 D # duplicate the current number
 sSè # and use one copy to index into
 •16|/• # 4335443554
 OO # sum digits and sum the stack

share

answered 5 mins ago

Emigna

43.9k431133

add a comment | 

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4 Answers
4

active

oldest

votes

4 Answers
4

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

Pip, 21 bytes

Lai+:$+4335443554@^Pi

Takes input $n$ as a command-line argument and outputs the first $n$ terms. Try it online!

Explanation

Lai+:$+4335443554@^Pi
 a is 1st cmdline arg; i is 0 (implicit)
La Loop (a) times:
 Pi Print i
 ^ Split it into a list of characters (i.e. digits)
 4335443554@ Use each digit to index into this number, giving the length of the
 name of the digit (0 -> 4, 1 -> 3, etc.)
 $+ Sum the results
 i+: Increment i by that amount

share|improve this answer

answered 35 mins ago

DLosc

18.5k33588

add a comment | 

up vote
2
down vote

Pip, 21 bytes

Lai+:$+4335443554@^Pi

Takes input $n$ as a command-line argument and outputs the first $n$ terms. Try it online!

Explanation

Lai+:$+4335443554@^Pi
 a is 1st cmdline arg; i is 0 (implicit)
La Loop (a) times:
 Pi Print i
 ^ Split it into a list of characters (i.e. digits)
 4335443554@ Use each digit to index into this number, giving the length of the
 name of the digit (0 -> 4, 1 -> 3, etc.)
 $+ Sum the results
 i+: Increment i by that amount

share|improve this answer

answered 35 mins ago

DLosc

18.5k33588

add a comment | 

up vote
2
down vote

up vote
2
down vote

Pip, 21 bytes

Lai+:$+4335443554@^Pi

Takes input $n$ as a command-line argument and outputs the first $n$ terms. Try it online!

Explanation

Lai+:$+4335443554@^Pi
 a is 1st cmdline arg; i is 0 (implicit)
La Loop (a) times:
 Pi Print i
 ^ Split it into a list of characters (i.e. digits)
 4335443554@ Use each digit to index into this number, giving the length of the
 name of the digit (0 -> 4, 1 -> 3, etc.)
 $+ Sum the results
 i+: Increment i by that amount

share|improve this answer

answered 35 mins ago

DLosc

18.5k33588

Pip, 21 bytes

Lai+:$+4335443554@^Pi

Takes input $n$ as a command-line argument and outputs the first $n$ terms. Try it online!

Explanation

Lai+:$+4335443554@^Pi
 a is 1st cmdline arg; i is 0 (implicit)
La Loop (a) times:
 Pi Print i
 ^ Split it into a list of characters (i.e. digits)
 4335443554@ Use each digit to index into this number, giving the length of the
 name of the digit (0 -> 4, 1 -> 3, etc.)
 $+ Sum the results
 i+: Increment i by that amount

share|improve this answer

answered 35 mins ago

DLosc

18.5k33588

share|improve this answer

share|improve this answer

answered 35 mins ago

DLosc

18.5k33588

answered 35 mins ago

DLosc

18.5k33588

answered 35 mins ago

DLosc

18.5k33588

18.5k33588

add a comment | 

add a comment | 

up vote
1
down vote

JavaScript (Node.js), 82 bytes

f=(a,b=1,s=4)=>a?b<a?f(a,++b,s+=[...s+''].reduce((q,w)=>+'4335443554'[w]+q,0)):s:0

Try it online!

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

add a comment | 

up vote
1
down vote

JavaScript (Node.js), 82 bytes

f=(a,b=1,s=4)=>a?b<a?f(a,++b,s+=[...s+''].reduce((q,w)=>+'4335443554'[w]+q,0)):s:0

Try it online!

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

add a comment | 

up vote
1
down vote

up vote
1
down vote

JavaScript (Node.js), 82 bytes

f=(a,b=1,s=4)=>a?b<a?f(a,++b,s+=[...s+''].reduce((q,w)=>+'4335443554'[w]+q,0)):s:0

Try it online!

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

JavaScript (Node.js), 82 bytes

f=(a,b=1,s=4)=>a?b<a?f(a,++b,s+=[...s+''].reduce((q,w)=>+'4335443554'[w]+q,0)):s:0

Try it online!

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

share|improve this answer

share|improve this answer

edited 1 hour ago

edited 1 hour ago

edited 1 hour ago

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

answered 1 hour ago

Luis felipe De jesus Munoz

3,36111049

3,36111049

add a comment | 

add a comment | 

up vote
1
down vote

Jelly, 13 bytes

ṃ“vẋç’ḃ5¤S+Ɗ¡

Try it online!

0-indexed.

Full program; takes input from STDIN.

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Erik the Outgolfer

29.8k42899

add a comment | 

up vote
1
down vote

Jelly, 13 bytes

ṃ“vẋç’ḃ5¤S+Ɗ¡

Try it online!

0-indexed.

Full program; takes input from STDIN.

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Erik the Outgolfer

29.8k42899

add a comment | 

up vote
1
down vote

up vote
1
down vote

Jelly, 13 bytes

ṃ“vẋç’ḃ5¤S+Ɗ¡

Try it online!

0-indexed.

Full program; takes input from STDIN.

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Erik the Outgolfer

29.8k42899

Jelly, 13 bytes

ṃ“vẋç’ḃ5¤S+Ɗ¡

Try it online!

0-indexed.

Full program; takes input from STDIN.

share|improve this answer

edited 1 hour ago

answered 1 hour ago

Erik the Outgolfer

29.8k42899

share|improve this answer

share|improve this answer

edited 1 hour ago

edited 1 hour ago

edited 1 hour ago

answered 1 hour ago

Erik the Outgolfer

29.8k42899

answered 1 hour ago

Erik the Outgolfer

29.8k42899

answered 1 hour ago

Erik the Outgolfer

29.8k42899

29.8k42899

add a comment | 

add a comment | 

up vote
0
down vote

05AB1E, 15 bytes

ÎFD•16|/•sSèOO

Try it online!

Explanation

Î # initialize stack with 0 and input
 F # input times do:
 D # duplicate the current number
 sSè # and use one copy to index into
 •16|/• # 4335443554
 OO # sum digits and sum the stack

share

answered 5 mins ago

Emigna

43.9k431133

add a comment | 

up vote
0
down vote

05AB1E, 15 bytes

ÎFD•16|/•sSèOO

Try it online!

Explanation

Î # initialize stack with 0 and input
 F # input times do:
 D # duplicate the current number
 sSè # and use one copy to index into
 •16|/• # 4335443554
 OO # sum digits and sum the stack

share

answered 5 mins ago

Emigna

43.9k431133

add a comment | 

up vote
0
down vote

up vote
0
down vote

05AB1E, 15 bytes

ÎFD•16|/•sSèOO

Try it online!

Explanation

Î # initialize stack with 0 and input
 F # input times do:
 D # duplicate the current number
 sSè # and use one copy to index into
 •16|/• # 4335443554
 OO # sum digits and sum the stack

share

answered 5 mins ago

Emigna

43.9k431133

05AB1E, 15 bytes

ÎFD•16|/•sSèOO

Try it online!

Explanation

Î # initialize stack with 0 and input
 F # input times do:
 D # duplicate the current number
 sSè # and use one copy to index into
 •16|/• # 4335443554
 OO # sum digits and sum the stack

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answered 5 mins ago

Emigna

43.9k431133

share

share

answered 5 mins ago

Emigna

43.9k431133

answered 5 mins ago

Emigna

43.9k431133

answered 5 mins ago

Emigna

43.9k431133

43.9k431133

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