OFFSET

1,2

COMMENTS

Do all the positive integers appear in this sequence?

With 10^6 terms, 87, 89, 90, 91, 92, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 108, 109, 110, 112 are the smallest numbers that still are not in the sequence.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A348400

EXAMPLE

a(8) = 29 and digitsum(29) = 11 is already in the sequence, so a(9) = a(8) + 8 = 29 + 8 = 37.

a(9) = 37 and digitsum(37) = 3 + 7 = 10 is not yet in the sequence, so a(10) = 10.

Written as an irregular triangle, in which each line begins with a term which is the digit sum of its preceding term, the sequence begins:

1, 2, 4, 7, 11, 16, 22, 29, 37;

10, 20, 31, 43, 56, 70, 85;

13, 30;

3, 22, 42;

6, 28, 51, 75;

12, 38, 65, 93, 122;

5, 36;

9, 42, 76, 111, 147, 184, 222, 261, 301, 342, 384;

15, 59;

14, 60, 107;

...

MATHEMATICA

seq[len_] := Module[{s = {1}, k, d, i = 1}, While[Length[s] < len, k = s[[-1]]; If[MemberQ[s, (d = Plus @@ IntegerDigits[k])], AppendTo[s, k + i], AppendTo[s, d]]; i++]; s]; seq[50] (* Amiram Eldar, Oct 21 2021 *)

PROG

(PARI) See Links section.

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Rodolfo Kurchan, Oct 21 2021

EXTENSIONS

Definition clarified by Amiram Eldar, Oct 23 2021

STATUS

approved