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%I #22 Oct 08 2023 09:06:07
%S 0,5,93448,39545957,240439822,1894541497,132563927578
%N Nonnegative integers k such that the sum of the first k primes is a hexagonal number.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hexagonal_number">Hexagonal number</a>.
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%e 5 is a term because the sum of the first five primes (2 + 3 + 5 + 7 + 11 = 28) is a hexagonal number.
%t A366270list[kmax_]:=Module[{p=0},Join[{0},Table[If[IntegerQ[(Sqrt[8(p+=Prime[k])+1]+1)/4],k,Nothing],{k,kmax}]]];A366270list[10^5]
%Y Subsequence of A175133.
%Y Cf. A000384, A007504, A033997, A364695, A364696, A366269 (corresponding hexagonal numbers).
%K nonn,hard,more
%O 1,2
%A _Paolo Xausa_, Oct 06 2023
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