%I #15 Mar 30 2024 17:12:37

%S 6,31,112,279,652,1231,2140,3363,5132,7647,10600,14583,19754,25435,

%T 31894,40617,50866,62583,76174,91431,108124,127319,147868,172493,

%U 200392,230281,262140,297413,334756,374607,419958,471113,524892,583853,649458,717339,790760,868997,951672,1039871,1134792

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

%H Robert Israel, <a href="/A337574/b337574.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p P:= <seq(ithprime(i), i=1..500)>:

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

%t Table[Prime[Range[n]].Prime[Range[n+1,2n]],{n,50}] (* _Harvey P. Dale_, Mar 30 2024 *)

%o (PARI) a(n) = sum(k=1, n, prime(k)*prime(n+k)); \\ _Michel Marcus_, Sep 02 2020

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

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

%K nonn

%O 1,1

%A _Robert Israel_, Sep 01 2020