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A072123
Remainder when Fibonacci(n) is divided by prime(n).
4
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
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
KEYWORD
easy,nonn
AUTHOR
Randy L. Ekl, Jun 20 2002
STATUS
approved