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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]+1), listput(v, s))); Vec(v ); \\ Jinyuan Wang, Oct 21 2021
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Will Do all other positive integers appear in this sequence?
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We multiply the last number by 2 and add a(1) = 1, ; if the sum of the digits of the new number 2*a(n-1) + 1 is not yet in the sequence, then this will be the next number in the sequence, if it already a(n) = 2*a(n-1) + 1; otherwise a(n) is in the sequence we continue multiplicating the last number by 2 and add sum of digits of a(n-1).
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Numbers of the form 2 + 3*k will not appear in this sequencessequence.
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