This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111136 #30 Jul 20 2025 15:16:28
%S A111136 1,3,8,21,110,343,1940,6121,34778,549007,1895276,26053093,191633234,
%T A111136 625127671,3596342744,56912633917,1013634659958,3518365441919,
%U A111136 48463935654772,356525456824901,1163040989874294,15635375014550515,114830228109306012,1894809644114020201
%N A111136 a(n) = Sum_{k=1..n} Fibonacci(prime(k)).
%H A111136 Robert Israel, <a href="/A111136/b111136.txt">Table of n, a(n) for n = 1..641</a>
%F A111136 a(n) = Sum_{i=1..n} A000045(A000040(i)). - _Wesley Ivan Hurt_, Feb 02 2014
%e A111136 The first 3 primes are 2, 3 and 5. So a(3) = F(2)+F(3)+F(5) = 1+2+5 = 8.
%p A111136 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 A111136 # second Maple program:
%p A111136 a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+
%p A111136 (<<0|1>, <1|1>>^ithprime(n))[1, 2])
%p A111136 end:
%p A111136 seq(a(n), n=1..25); # _Alois P. Heinz_, Jun 24 2022
%t A111136 f[n_] := Sum[ Fibonacci[ Prime[i]], {i, n}]; Array[f, 22] (* _Robert G. Wilson v_, Oct 21 2005 *)
%Y A111136 Cf. A000040, A000045.
%Y A111136 Partial sums of A030426.
%K A111136 nonn
%O A111136 1,2
%A A111136 _Leroy Quet_, Oct 17 2005
%E A111136 More terms from _Robert G. Wilson v_, Oct 21 2005