cp's OEIS Frontend

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

%I A131073 #21 Mar 07 2024 11:13:13
%S A131073 2,3,5,8,11,15,19,24,29,35,41,48,55,62,69,76,83,91,99,107,116,125,134,
%T A131073 143,152,161,170,179,189,199,210,221,232,243,254,265,276,287,298,309,
%U A131073 320,331,343,355,367,380,393,406,419,433,448,463,479,496,513,530,547
%N A131073 a(1)=2. a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are prime).
%C A131073 By Dirichlet's Theorem, there are an infinite number of primes in this sequence.
%H A131073 Reinhard Zumkeller, <a href="/A131073/b131073.txt">Table of n, a(n) for n = 1..10000</a>
%F A131073 a(n+1) = a(n) + Sum_{k=1..n} A010051(a(k)). - _Reinhard Zumkeller_, Nov 15 2011
%e A131073 There are 5 primes (2,3,5,11,19) among the first 7 terms of the sequence. So a(8) = a(7) + 5 = 24.
%t A131073 f[lst_] := Append[lst, Last@lst + Length@ Select[lst, PrimeQ@# &]]; Nest[f, {2}, 56] (* _Robert G. Wilson v_, Jul 02 2007 *)
%o A131073 (Haskell)
%o A131073 a131073 n = a131073_list !! (n-1)
%o A131073 a131073_list = 2 : f 2 1 where
%o A131073    f x c = y : f y (c + a010051 y) where y = x + c
%o A131073 -- _Reinhard Zumkeller_, Nov 15 2011
%Y A131073 Cf. A010051, A097602.
%K A131073 nonn
%O A131073 1,1
%A A131073 _Leroy Quet_, Jun 13 2007
%E A131073 More terms from _Robert G. Wilson v_, Jul 02 2007