A172167 Partial sums of Class 1- (or Pierpont) primes A005109.

2, 5, 10, 17, 30, 47, 66, 103, 176, 273, 382, 545, 738, 995, 1428, 1915, 2492, 3261, 4414, 5711, 7170, 9763, 12680, 16137, 20026, 30395, 42684, 60181, 78614, 117981, 170470, 236007, 375976, 523433, 733386, 1065163, 1537556, 2167413, 2913910

Offset

1,1

Comments

The subsequence of primes in this sequence begins a(1) = 2, a(2) = 5, a(4) = 17, a(6) = 47, a(8) = 103, a(20) = 5711. The subsubsequence which are Pierpont prime partial sums of Pierpont primes begins 2, 5, 17, and then which occur next?

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = SUM[i=1..n] A005109(i) = SUM[i=1..n] (primes of the form 2^t*3^u + 1}.

Example

a(20) = 2 + 3 + 5 + 7 + 13 + 17 + 19 + 37 + 73 + 97 + 109 + 163 + 193 + 257 + 433 + 487 + 577 + 769 + 1153 + 1297 = 5711 is prime.

Crossrefs

Cf. A000040, A048135, A048136, A056637, A005105, A005110, A005111, A005112, A081424, A081425, A081426, A081427, A081428, A081429, A081430, A122259.

Sequence in context: A294562 A109377 A109472 * A173060 A173520 A360749

Adjacent sequences: A172164 A172165 A172166 * A172168 A172169 A172170

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 28 2010

Extensions

More terms from R. J. Mathar, Feb 07 2010

Status

approved