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A131073 a(1)=2. a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are prime). 4
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 (list; graph; refs; listen; history; text; internal format)
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(A010051(a(k)): 1 <= k <= n). - 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. A097602.

Sequence in context: A194248 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

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Last modified August 18 22:09 EDT 2017. Contains 290768 sequences.