A111136 - OEIS

%I #24 Jun 24 2022 19:11:39

%S 1,3,8,21,110,343,1940,6121,34778,549007,1895276,26053093,191633234,

%T 625127671,3596342744,56912633917,1013634659958,3518365441919,

%U 48463935654772,356525456824901,1163040989874294,15635375014550515,114830228109306012,1894809644114020201

%N a(n) = Sum_{k=1..n} Fibonacci(prime(k)).

%F a(n) = Sum_{i=1..n} A000045(A000040(i)). - _Wesley Ivan Hurt_, Feb 02 2014

%e The first 3 primes are 2, 3 and 5. So a(3) = F(2)+F(3)+F(5) = 1+2+5 = 8.

%p with(numtheory); with(combinat); A111136:=n->sum(fibonacci(ithprime(i)), i=1..n); seq(A111136(n), n=1..30); # _Wesley Ivan Hurt_, Feb 02 2014

%p # second Maple program:

%p a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+

%p       (<<0|1>, <1|1>>^ithprime(n))[1, 2])

%p     end:

%p seq(a(n), n=1..25);  # _Alois P. Heinz_, Jun 24 2022

%t f[n_] := Sum[ Fibonacci[ Prime[i]], {i, n}]; Array[f, 22] (* _Robert G. Wilson v_ *)

%Y Cf. A000040, A000045.

%Y Partial sums of A030426.

%K nonn

%O 1,2

%A _Leroy Quet_, Oct 17 2005

%E More terms from _Robert G. Wilson v_, Oct 21 2005