A349548 First column of A348575.

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

Author

Rodolfo Kurchan, Nov 21 2021

Keywords

• nonn
• base
• hard
• more

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