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

Author

Dumitru Damian, Aug 22 2021

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = my(p=prime(n)); p*(5*p-3)/2; \\ Michel Marcus, Sep 16 2021

Python

from sympy import primerange
print([p*(5*p-3)//2 for p in primerange(1, 180)]) # Michael S. Branicky, Aug 22 2021

Sage

A = [int(p*(5*p-3)/2) for p in range(0,10^3) if p in Primes()]

Formula

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