

A131073


a(1)=2. a(n) = a(n1) + (number of terms, from among terms a(1) through a(n1), 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
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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 !! (n1)
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: 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



