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A364694
Polygonal numbers of order greater than 2 (A090466) which are the sum of the first k primes, for some k > 0.
4
10, 28, 58, 100, 129, 160, 238, 328, 381, 501, 568, 639, 712, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 2127, 2276, 2427, 2584, 2914, 3087, 3447, 3831, 4227, 4438, 4888, 5350, 5589, 5830, 6081, 6601, 6870, 8275, 10191, 10887, 11599, 12339, 12718
OFFSET
1,1
EXAMPLE
28 is a term because it's both a triangular number and the sum of the first 5 primes (2 + 3 + 5 + 7 + 11).
58 is a term because it's both an octagonal number and the sum of the first 7 primes (2 + 3 + 5 + 7 + 11 + 13 + 17).
MATHEMATICA
A364693Q[n_]:=With[{d=Divisors[2n]}, Catch[For[i=3, i<Length[d]-1, i++, If[Divisible[2n/d[[i]]-2, d[[i]]-1], Throw[True]]]; False]]; (* After Jianing Song in A090466 *)
A364694list[kmax_]:=Select[Accumulate[Prime[Range[kmax]]], A364693Q]; A364694list[100]
CROSSREFS
Intersection of A007504 with A090466.
Sequence in context: A169879 A054112 A053790 * A269441 A048491 A124703
KEYWORD
nonn
AUTHOR
Paolo Xausa, Aug 03 2023
STATUS
approved