A337574 a(n) is the dot product of the vectors of the first n primes and the next n primes.

6, 31, 112, 279, 652, 1231, 2140, 3363, 5132, 7647, 10600, 14583, 19754, 25435, 31894, 40617, 50866, 62583, 76174, 91431, 108124, 127319, 147868, 172493, 200392, 230281, 262140, 297413, 334756, 374607, 419958, 471113, 524892, 583853, 649458, 717339, 790760, 868997, 951672, 1039871, 1134792

Offset: 1

Author

Robert Israel, Sep 01 2020

Keywords

• nonn

Examples

			a(3) = 2*7 + 3*11 + 5*13 = 112.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A337573 (n such that a(n) is prime).

Cf. A033994 (similar when prime(n) is replaced with n).

Programs

Maple

P:= :
[seq(P[1..t]^%T . P[t+1..2*t],t=1..250)];

Mathematica

Table[Prime[Range[n]].Prime[Range[n+1,2n]],{n,50}] (* Harvey P. Dale, Mar 30 2024 *)

PARI

a(n) = sum(k=1, n, prime(k)*prime(n+k)); \\ Michel Marcus, Sep 02 2020

Formula

a(n) = Sum_{k=1..n} prime(k)*prime(n+k).