A121104 a(n) = Fibonacci(n - 1) modulo the n-th prime number.

1, 1, 2, 3, 5, 8, 13, 21, 5, 24, 15, 21, 18, 1, 27, 43, 11, 38, 63, 49, 44, 32, 88, 2, 83, 59, 73, 76, 79, 63, 113, 9, 94, 61, 6, 123, 76, 149, 127, 34, 74, 124, 32, 83, 1, 3, 91, 212, 204, 232, 85, 76, 171, 141, 148, 234, 145, 38, 2, 271, 208, 179, 194, 73, 14, 127, 177

Offset: 2

Author

Gil Broussard, Aug 12 2006

Keywords

• nonn

Examples

			a(10)=5 because the 9th Fibonacci=34, the 10th Prime=29, and 34 mod 29=5.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..5000

Crossrefs

Cf. A000040, A000045, A072123.

Programs

Magma

[Fibonacci(n-1) mod NthPrime(n): n in [2..70]]; // Vincenzo Librandi, Jun 19 2017

Mathematica

With[{nn=70},Mod[First[#],Last[#]]&/@Thread[{Fibonacci[Range[nn-1]], Prime[ Range[2,nn]]}]] (* Harvey P. Dale, Feb 27 2013 *)
Table[Mod[Fibonacci[n - 1], Prime[n]], {n, 2, 70}] (* Vincenzo Librandi, Jun 19 2017 *)

PARI

a(n) = fibonacci(n-1) % prime(n); \\ Michel Marcus, Jun 18 2017

PARI

fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
a(n)=lift(fibmod(n-1,prime(n))) \\ Charles R Greathouse IV, Jun 19 2017

Formula

a(n) = Fibonacci(n - 1) modulo Prime(n).