A096277 Sum of successive sums of successive primes: a(n) = s(n) + s(n+1) where s(n) = prime(n) + prime(n+1) (A001043).

13, 20, 30, 42, 54, 66, 78, 94, 112, 128, 146, 162, 174, 190, 212, 232, 248, 266, 282, 296, 314, 334, 358, 384, 402, 414, 426, 438, 462, 498, 526, 544, 564, 588, 608, 628, 650, 670, 692, 712, 732, 756, 774, 786, 806, 844, 884, 906, 918, 934

Offset: 1

Author

Cino Hilliard, Jun 22 2004

Keywords

• easy
• nonn

Comments

The first term is the only term that has a chance of being prime.

Examples

			The sums of the first two pairs of successive primes are 5 and 8. 5+8 = 13 is the first term in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001043, A000040.

Programs

Mathematica

Total/@Partition[Total/@Partition[Prime[Range[60]],2,1],2,1] (* Harvey P. Dale, May 10 2011 *)
Nest[ListConvolve[{1,1},#]&,Prime[Range[100]],2] (* Paolo Xausa, Oct 31 2023 *)

PARI

f1(n,f(n)=prime(n)+prime(n+1)) = for(x=1,n,print(f(x)+f(x+1)","))

Formula

a(n) = A001043(n) + A001043(n+1) = A000040(n) + 2*A000040(n+1) + A000040(n+2). - M. F. Hasler, Jun 02 2017

Extensions

Edited by M. F. Hasler, Jun 02 2017