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

Author

Ilya Gutkovskiy, Jan 12 2016

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Decagonal Number
• Eric Weisstein's World of Mathematics, Prime Number

Crossrefs

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

Programs

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 *)

PARI

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

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)).