A083215 a(n) = 1 + Sum(prime(i)*(2*i-1): 1<=i<=n).

3, 12, 37, 86, 185, 328, 549, 834, 1225, 1776, 2427, 3278, 4303, 5464, 6827, 8470, 10417, 12552, 15031, 17800, 20793, 24190, 27925, 32108, 36861, 42012, 47471, 53356, 59569, 66236, 73983, 82236, 91141, 100454, 110735, 121456, 132917

Offset: 1

Author

Reinhard Zumkeller, Jun 01 2003

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Figurate Number.

Crossrefs

Cf. A002412.

Equals 1 + A316322(n).

Programs

Mathematica

nxt[{n_, a_}] := {n + 1, a + Prime[n + 1] (2 n + 1)}; NestList[nxt,{1,2},50][[All,2]]+1 (* Harvey P. Dale, Jul 05 2018 *)

PARI

a(n) = 1 + sum(i=1, n, prime(i)*(2*i-1)); \\ Michel Marcus, Jan 22 2022

Extensions

Definition corrected by Harvey P. Dale, Jul 03 2018