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

Author

Cino Hilliard, May 03 2005

Keywords

• easy
• nonn

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Fibonacci Number.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

Corrected by T. D. Noe, Nov 15 2006