A105554 Primes whose indices are the sum of the first n+1 Fibonacci numbers.

2, 3, 7, 17, 37, 71, 137, 251, 457, 823, 1459, 2579, 4483, 7789, 13463, 23143, 39769, 67927, 115823, 196681, 333227, 563971, 951553, 1603471, 2696653, 4528921, 7594759, 12717701, 21275489, 35548187, 59328121, 98921047, 164781917

Offset

1,1

Comments

We avoid testing for existence in the script by beginning with x=1.

Sum[i=1 to n+1]F(i) = F(n+3) - 1. See equation (18) of the Weisstein reference. - Jonathan Vos Post, May 05 2005

Links

Table of n, a(n) for n=1..33.

Eric Weisstein's World of Mathematics, Fibonacci Number.

Formula

a(n) = prime(F(n+3) - 1) = A000040(A000045(n+3)-1). - Jonathan Vos Post, May 05 2005

Example

a(1) = prime(Fibonacci(0) + Fibonacci(1)) = prime(0+1) = prime(1) = 2.
a(3) = prime(Fibonacci(0) + Fibonacci(1) + Fibonacci(2) + Fibonacci(3)) = prime(4) = 7.

Mathematica

Prime[Accumulate[Fibonacci[Range[40]]]] (* Harvey P. Dale, Aug 14 2023 *)

Prog

(PARI) g(n) = s=0; for(x=1, n, s+=fibonacci(x); print1(prime(s)", "))

Crossrefs

Sequence in context: A267601 A155548 A191033 * A145230 A135364 A051291

Adjacent sequences: A105551 A105552 A105553 * A105555 A105556 A105557

Keyword

easy,nonn

Author

Cino Hilliard, May 03 2005

Extensions

Corrected by T. D. Noe, Nov 15 2006

Status

approved