A172112 Partial sums of A023200.

3, 10, 23, 42, 79, 122, 189, 268, 365, 468, 577, 704, 867, 1060, 1283, 1512, 1789, 2096, 2409, 2758, 3137, 3534, 3973, 4430, 4893, 5380, 5879, 6492, 7135, 7808, 8547, 9304, 10073, 10896, 11749, 12608, 13485, 14368, 15275, 16212, 17179, 18188, 19275

Offset: 1

Author

Jonathan Vos Post, Jan 25 2010

Keywords

• easy
• nonn

Comments

Primes in the partial sum begin: a(1) = 3, a(3) = 23, a(5) = 79, a(11) = 577, a(15) = 1283, a(17) = 1789, a(21) = 3137, a(27) = 5879. Of these, the smaller members of cousin prime pairs which appear among the partial sums of smaller member p of cousin prime pairs begin: 3, 79; which are the next in this subset?

Examples

			a(30) = 3 + 7 + 13 + 19 + 37 + 43 + 67 + 79 + 97 + 103 + 109 + 127 + 163 + 193 + 223 + 229 + 277 + 307 + 313 + 349 + 379 + 397 + 439 + 457 + 463 + 487 + 499 + 613 + 643 + 673 = 7808.
		

Crossrefs

Cf. A000040, A023200, A046132.

Programs

Mathematica

Accumulate[Select[Prime[Range[250]],PrimeQ[#+4]&]] (* Harvey P. Dale, Oct 09 2023 *)

Formula

a(n) = SUM[i=i..n] A023200(i) = SUM[i=i..n] {Primes p such that p and p + 4 are both primes}.

Extensions

More terms from Max Alekseyev, Jan 31 2010