A121104 - OEIS

%I #30 Sep 08 2022 08:45:27

%S 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,

%T 73,76,79,63,113,9,94,61,6,123,76,149,127,34,74,124,32,83,1,3,91,212,

%U 204,232,85,76,171,141,148,234,145,38,2,271,208,179,194,73,14,127,177

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

%H Vincenzo Librandi, <a href="/A121104/b121104.txt">Table of n, a(n) for n = 2..5000</a>

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

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

%t With[{nn=70},Mod[First[#],Last[#]]&/@Thread[{Fibonacci[Range[nn-1]], Prime[ Range[2,nn]]}]] (* _Harvey P. Dale_, Feb 27 2013 *)

%t Table[Mod[Fibonacci[n - 1], Prime[n]], {n, 2, 70}] (* _Vincenzo Librandi_, Jun 19 2017 *)

%o (PARI) a(n) = fibonacci(n-1) % prime(n); \\ _Michel Marcus_, Jun 18 2017

%o (PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]

%o a(n)=lift(fibmod(n-1,prime(n))) \\ _Charles R Greathouse IV_, Jun 19 2017

%o (Magma) [Fibonacci(n-1) mod NthPrime(n): n in [2..70]]; // _Vincenzo Librandi_, Jun 19 2017

%Y Cf. A000040, A000045, A072123.

%K nonn

%O 2,3

%A _Gil Broussard_, Aug 12 2006