A346494 Heptagonal numbers (A000566) with prime indices (A000040).

7, 18, 55, 112, 286, 403, 697, 874, 1288, 2059, 2356, 3367, 4141, 4558, 5452, 6943, 8614, 9211, 11122, 12496, 13213, 15484, 17098, 19669, 23377, 25351, 26368, 28462, 29539, 31753, 40132, 42706, 46717, 48094, 55279, 56776, 61387, 66178, 69472, 74563, 79834

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Formula

a(n) = A000566(A000040(n)) = prime(n)*(5*prime(n)-3)/2.

Example

a(1) = Heptagonal(prime(1)) = A000566(2) = 2*(5*2-3)/2 = 7;
a(2) = Heptagonal(prime(2)) = A000566(3) = 3*(5*3-3)/2 = 18;
a(3) = Heptagonal(prime(3)) = A000566(5) = 5*(5*5-3)/2 = 55.

Mathematica

A346494[n_] := PolygonalNumber[7, Prime[n]]; Table[A346494[n], {n, 1, 41}] (* Robert P. P. McKone, Aug 22 2021 *)

Prog

(Sage)
A = [int(p*(5*p-3)/2) for p in range(0, 10^3) if p in Primes()]
(Python)
from sympy import primerange
print([p*(5*p-3)//2 for p in primerange(1, 180)]) # Michael S. Branicky, Aug 22 2021
(PARI) a(n) = my(p=prime(n)); p*(5*p-3)/2; \\ Michel Marcus, Sep 16 2021

Crossrefs

Cf. A000566, A034953, A001248, A116995, A117961, A267144.

Sequence in context: A343545 A324944 A084819 * A220031 A197092 A288743

Adjacent sequences: A346491 A346492 A346493 * A346495 A346496 A346497

Keyword

nonn,easy

Author

Dumitru Damian, Aug 22 2021

Status

approved