A131073 a(1)=2. a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are prime).

2, 3, 5, 8, 11, 15, 19, 24, 29, 35, 41, 48, 55, 62, 69, 76, 83, 91, 99, 107, 116, 125, 134, 143, 152, 161, 170, 179, 189, 199, 210, 221, 232, 243, 254, 265, 276, 287, 298, 309, 320, 331, 343, 355, 367, 380, 393, 406, 419, 433, 448, 463, 479, 496, 513, 530, 547

Offset

1,1

Comments

By Dirichlet's Theorem, there are an infinite number of primes in this sequence.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n+1) = a(n) + Sum_{k=1..n} A010051(a(k)). - Reinhard Zumkeller, Nov 15 2011

Example

There are 5 primes (2,3,5,11,19) among the first 7 terms of the sequence. So a(8) = a(7) + 5 = 24.

Mathematica

f[lst_] := Append[lst, Last@lst + Length@ Select[lst, PrimeQ@# &]]; Nest[f, {2}, 56] (* Robert G. Wilson v, Jul 02 2007 *)

Prog

(Haskell)
a131073 n = a131073_list !! (n-1)
a131073_list = 2 : f 2 1 where
   f x c = y : f y (c + a010051 y) where y = x + c
-- Reinhard Zumkeller, Nov 15 2011

Crossrefs

Cf. A010051, A097602.

Sequence in context: A325515 A126097 A024611 * A062485 A175143 A137179

Adjacent sequences: A131070 A131071 A131072 * A131074 A131075 A131076

Keyword

nonn

Author

Leroy Quet, Jun 13 2007

Extensions

More terms from Robert G. Wilson v, Jul 02 2007

Status

approved