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A105554
Primes whose indices are the sum of the first n+1 Fibonacci numbers.
1
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
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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, May 03 2005
EXTENSIONS
Corrected by T. D. Noe, Nov 15 2006
STATUS
approved