A267217 10-gonal (or decagonal) numbers with prime indices.

10, 27, 85, 175, 451, 637, 1105, 1387, 2047, 3277, 3751, 5365, 6601, 7267, 8695, 11077, 13747, 14701, 17755, 19951, 21097, 24727, 27307, 31417, 37345, 40501, 42127, 45475, 47197, 50737, 64135, 68251, 74665, 76867, 88357, 90751, 98125, 105787, 111055, 119197, 127627, 130501, 145351, 148417, 154645

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Decagonal Number

Eric Weisstein's World of Mathematics, Prime Number

Formula

a(n) = prime(n)*(4*prime(n) - 3) = A000040(n)*(4*A000040(n) - 4).

a(n) = A001107(A000040(n)).

a(n) = sigma_0(48^(prime(n) - 1)) = A000005(A009992(A000040(n) - 1)).

Mathematica

Table[Prime[n] (4 Prime[n] - 3), {n, 1, 45}]
Module[{nn=200, pn}, pn=PolygonalNumber[10, Range[nn]]; Table[pn[[p]], {p, Prime[ Range[PrimePi[nn]]]}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 27 2020 *)

Prog

(PARI) lista(nn) = forprime(p=2, nn, print1(p*(4*p-3), ", ")); \\ Altug Alkan, Jan 12 2016

Crossrefs

Cf. A000040, A001107, A001248, A034953, A116995, A117961, A267144.

Sequence in context: A103135 A220021 A008468 * A179546 A119548 A219629

Adjacent sequences: A267214 A267215 A267216 * A267218 A267219 A267220

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Jan 12 2016

Status

approved