A074745 a(n) = sum_{k=1..n} prime(k)*prime(k+1).

6, 21, 56, 133, 276, 497, 820, 1257, 1924, 2823, 3970, 5487, 7250, 9271, 11762, 14889, 18488, 22575, 27332, 32515, 38282, 44839, 52226, 60859, 70656, 81059, 92080, 103743, 116060, 130411, 147048, 164995, 184038, 204749, 227248, 250955

Offset: 1

Author

Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 06 2002

Keywords

• nonn

Programs

Maple

with(numtheory): a := proc(n) local k: RETURN(add(ithprime(k)*ithprime(k+1),k=1..n)):end;

Mathematica

s=0;Table[s+=Prime[n]*Prime[n+1],{n,5!}] (* Vladimir Joseph Stephan Orlovsky, Nov 19 2010 *)

PARI

a(n) = sum(k=1, n, prime(k)*prime(k+1)); \\ Michel Marcus, Jan 16 2015

Formula

a(n) = Sum_{k=1..n} prime(k)*prime(k+1) = Sum_{k=1..n} A006094(k).