cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A349547 a(n) is the length of the n-th row of A348575.

Original entry on oeis.org

9, 28, 100, 3660, 2, 4, 34, 279, 1342, 24486, 41, 4, 9, 37, 3373, 30332, 10768, 89207, 9888780, 118322, 103912, 1083421, 1095431404, 1182371, 33970573, 116430219, 3152744167, 24330557, 27560841783
Offset: 1

Views

Author

Rodolfo Kurchan, Nov 21 2021

Keywords

Comments

Terms computed by Claudio Meller.

Examples

			When A348575 is written as an irregular triangle, the first three rows are:
   1, ...,   37:   9 terms
  10, ...,  388:  28 terms
  19, ..., 4969: 100 terms
The lengths of the rows are [9, 28, 100] respectively, the same as the first three terms of this sequence.
a(30) exceeds 4242640687120 (perhaps by orders of magnitude); see A349548. - _Jon E. Schoenfield_, Nov 29 2021
		

Crossrefs

Programs

  • Mathematica
    seq[len_] := Module[{s = {1}, sq = {}, i = 1, d}, While[Length[sq] < len, If[MemberQ[s, (d = Plus @@ IntegerDigits[s[[-1]]])], AppendTo[s, s[[-1]] + i], AppendTo[s, d]; AppendTo[sq, i]; i = 0]; i++]; sq]; seq[15] (* Amiram Eldar, Nov 23 2021 *)

Extensions

a(23)-a(29) from Jon E. Schoenfield, Nov 30 2021

A349548 First column of A348575.

Original entry on oeis.org

1, 10, 19, 28, 52, 8, 5, 17, 35, 44, 68, 24, 3, 12, 21, 51, 70, 58, 77, 107, 81, 75, 93, 144, 100, 118, 127, 151, 116, 167
Offset: 1

Views

Author

Rodolfo Kurchan, Nov 21 2021

Keywords

Comments

Terms computed by Claudio Meller.
From Jon E. Schoenfield, Nov 30 2021: (Start)
In A348575, row 30 begins with 167 == 5 (mod 9), so T(30, k) = 167 + A000217(k-1), hence a number whose digit sum is congruent to 2, 5, 6, or 8 (mod 9). After the first several terms of row 30, the smallest digit sums that have not yet appeared are 160, 169, 208, 214, 216, 219, 224, 226, 237, and 240; among those, the only ones congruent to 2, 5, 6, or 8 (mod 9) are 224 and 240, so it seems nearly certain that row 30 will end with the first term of A348575 whose digit sum is 224.
The smallest number whose digit sum is 224 is 8999999999999999999999999 = 9*10^24 - 1, so row 30 will have at least 4242640687120 terms. (The smallest number of the form 167 + A000217(k-1) whose digit sum is 224 seems likely to be a few orders of magnitude larger than 9*10^24.) (End)

Examples

			When A348575 is written as an irregular triangle, the first three rows start as:
   1,  2,  4, ...
  10, 11, 13, ...
  19, 20, 22, ...
The first numbers of the rows are [1, 10, 19] respectively, the same as the first three terms of this sequence.
		

Crossrefs

Column 1 of A348575.
Cf. A349547.

Programs

  • Mathematica
    seq[len_] := Module[{s = sq = {1}, i = 1, d}, While[Length[sq] < len, If[MemberQ[s, (d = Plus @@ IntegerDigits[s[[-1]]])], AppendTo[s, s[[-1]] + i], AppendTo[s, d]; AppendTo[sq, d]; i = 0]; i++]; sq]; seq[15] (* Amiram Eldar, Nov 23 2021 *)

Extensions

a(24)-a(30) from Jon E. Schoenfield, Nov 30 2021

A349742 Right border of A348575.

Original entry on oeis.org

37, 388, 4969, 6695998, 53, 14, 566, 38798, 899846, 299769899, 888, 30, 39, 678, 5686899, 459999997, 57969598, 3978899879, 48893979999887, 6999988788, 5398799997, 586899989985, 599984979886989999, 698999999779, 576999897988978, 6777997889978989
Offset: 1

Views

Author

Rodolfo Kurchan, Nov 28 2021

Keywords

Comments

Terms computed by Claudio Meller.

Crossrefs

Programs

  • Mathematica
    seq[len_] := Module[{s = {1}, sq = {}, i = 1, d}, While[Length[sq] < len, If[MemberQ[s, (d = Plus @@ IntegerDigits[s[[-1]]])], AppendTo[s, s[[-1]] + i], AppendTo[s, d]; AppendTo[sq, s[[-2]]]; i = 0]; i++]; sq]; seq[15] (* Amiram Eldar, Nov 30 2021 *)

Formula

a(n) = A349548(n) + A000217(A349547(n) - 1). - Jon E. Schoenfield, Nov 30 2021

Extensions

a(21)-a(26) from Jon E. Schoenfield, Nov 30 2021
Showing 1-3 of 3 results.