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

Author

Leroy Quet, Jun 13 2007

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A010051, A097602.

Programs

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

Mathematica

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

Formula

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

Extensions

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