A072123 Remainder when Fibonacci(n) is divided by prime(n).

1, 1, 2, 3, 5, 8, 13, 2, 11, 26, 27, 33, 28, 33, 46, 33, 4, 22, 27, 20, 69, 15, 22, 88, 44, 92, 100, 21, 76, 21, 69, 41, 116, 134, 44, 76, 70, 117, 80, 157, 129, 87, 73, 27, 157, 1, 5, 208, 27, 108, 1, 203, 230, 19, 112, 143, 206, 258, 31, 3, 146, 266, 117, 213, 211, 168

Offset

1,3

Comments

For k=0..8, a(10^k) = 1, 26, 55, 5965, 99584, 728618, 2256590, 61329731, 1081853265. - Zak Seidov, Dec 23 2014

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

a(n) = F(n) mod prime(n), where F(n) is the n-th Fibonacci number and prime(n) is the n-th prime number.

Example

a(8) = F(8) mod prime(8) = 21 mod 19 = 2.

Maple

seq(combinat[fibonacci](n) mod ithprime(n), n=1..1000); # Robert Israel, Dec 24 2014

Mathematica

Table[Mod[Fibonacci[n], Prime[n]], {n, 70}] (* Harvey P. Dale, Jan 25 2011 *)

Prog

(Magma) [Fibonacci(n) mod NthPrime(n): n in [1..120]]; // Vincenzo Librandi, Nov 19 2015
(PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
a(n)=lift(fibmod(n, prime(n))) \\ Charles R Greathouse IV, Jun 19 2017

Crossrefs

Cf. A000040, A000045, A075702 (locations of 0 in this sequence), A121104.

Sequence in context: A118604 A261694 A287533 * A135102 A214156 A078414

Adjacent sequences: A072120 A072121 A072122 * A072124 A072125 A072126

Keyword

easy,nonn

Author

Randy L. Ekl, Jun 20 2002

Status

approved