A348433 a(1) = 1; a(n+1) = 2*a(n) if the digit sum of a(n) is already in the sequence, otherwise a(n+1) = digitsum(a(n)).

1, 2, 4, 8, 16, 7, 14, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 11, 22, 44, 88, 176, 352, 704, 1408, 13, 26, 52, 104, 208, 416, 832, 1664, 17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 19, 38, 76, 152, 304, 608, 1216, 2432, 4864, 9728, 19456, 25, 50, 100, 200

Offset: 1

Author

Rodolfo Kurchan, Oct 18 2021

Keywords

• nonn
• base

Comments

There are no multiples of 3 in this sequence.

Will all other positive integers appear in this sequence?

Examples

			The sum of the digits of a(4) = 8 is 8, which is already in the sequence, so a(5) = 2*8 = 16.
The sum of the digits of a(5) = 16 is 7, which is not yet in the sequence, so a(6) = 7.
From _Omar E. Pol_, Oct 19 2021: (Start)
Written as an irregular triangle the sequence begins (see A348408):
   1,  2,  4,   8,  16;
   7, 14;
   5, 10, 20,  40,  80, 160,  320,  640, 1280;
  11, 22, 44,  88, 176, 352,  704, 1408;
  13, 26, 52, 104, 208, 416,  832, 1664;
  17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704;
  19, 38, 76, 152, 304, 608, 1216, 2432, 4864, 9728, 19456;
... (End)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A348433

Crossrefs

Cf. A001651, A007953, A008585, A331440 (similar), A348400, A348408, A348483.

Programs

Mathematica

seq[len_] := Module[{s = {1}, k, d}, While[Length[s] < len, k = s[[-1]]; If[MemberQ[s, (d = Plus @@ IntegerDigits[k])], AppendTo[s, 2*k], AppendTo[s, d]]]; s]; seq[50] (* Amiram Eldar, Oct 19 2021 *)

PARI

lista(nn) = my(s, v=List([1])); for(n=1, nn, if(setsearch(vecsort(v), s=sumdigits(v[n])), listput(v, 2*v[n]), listput(v, s))); v \\ Jinyuan Wang, Oct 21 2021

PARI

See Links section.

Extensions

Definition and examples clarified by N. J. A. Sloane, Oct 24 2021