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

1,1

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?

Links

Table of n, a(n) for n=1..43.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000040, A023200, A046132.

Sequence in context: A041403 A077126 A172113 * A227347 A068043 A145069

Adjacent sequences: A172109 A172110 A172111 * A172113 A172114 A172115

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 25 2010

Extensions

More terms from Max Alekseyev, Jan 31 2010

Status

approved