A051830 a(n) = Fibonacci(p(n)+1) mod p(n), where p(n) is the n-th prime.

0, 0, 3, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1

Offset: 1

Author

Jud McCranie, Dec 11 1999

Keywords

• nonn

Comments

Terms are 1 when p(n) == 1 or 4 (mod 5) and 0 when p(n) == 2 or 3 (mod 5).

Examples

			p(3) = 5, so a(3) = Fibonacci(5+1) mod 5 = 3.
		

Crossrefs

Cf. A000040, A000045, A003631, A045468, A051834, A051831.

Programs

Mathematica

Table[Mod[Fibonacci[n+1],n],{n,Prime[Range[110]]}] (* Harvey P. Dale, Nov 27 2015 *)

Formula

a(n) = max(0, Legendre(5,prime(n))) for n >= 4, where Legendre is the Legendre symbol. - Haifeng Xu, Jan 31 2025