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

2,3

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A000045, A072123.

Sequence in context: A327451 A137290 A268962 * A118627 A358404 A080787

Adjacent sequences: A121101 A121102 A121103 * A121105 A121106 A121107

Keyword

nonn

Author

Gil Broussard, Aug 12 2006

Status

approved