A111136 a(n) = Sum_{k=1..n} Fibonacci(prime(k)).

1, 3, 8, 21, 110, 343, 1940, 6121, 34778, 549007, 1895276, 26053093, 191633234, 625127671, 3596342744, 56912633917, 1013634659958, 3518365441919, 48463935654772, 356525456824901, 1163040989874294, 15635375014550515, 114830228109306012, 1894809644114020201

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..641

Formula

a(n) = Sum_{i=1..n} A000045(A000040(i)). - Wesley Ivan Hurt, Feb 02 2014

Example

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

Maple

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
# Alternative:
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+
      (<<0|1>, <1|1>>^ithprime(n))[1, 2])
    end:
seq(a(n), n=1..25);  # Alois P. Heinz, Jun 24 2022

Mathematica

f[n_] := Sum[ Fibonacci[ Prime[i]], {i, n}]; Array[f, 22] (* Robert G. Wilson v, Oct 21 2005 *)

Prog

(PARI) a(n) = sum(k=1, n, fibonacci(prime(k))) \\ Bruce Nye, Feb 25 2026

Crossrefs

Cf. A000040, A000045.

Partial sums of A030426.

Sequence in context: A361574 A353424 A156291 * A374340 A348636 A063937

Adjacent sequences: A111133 A111134 A111135 * A111137 A111138 A111139

Keyword

nonn

Author

Leroy Quet, Oct 17 2005

Extensions

More terms from Robert G. Wilson v, Oct 21 2005

Status

approved