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A348433
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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)).
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6
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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
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listen;
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internal format)
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OFFSET
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1,2
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COMMENTS
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There are no multiples of 3 in this sequence.
Will all other positive integers appear in this sequence?
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LINKS
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EXAMPLE
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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.
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)
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MATHEMATICA
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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 *)
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PROG
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(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.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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