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

%I A072123 #39 Apr 03 2025 18:22:13
%S A072123 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,
%T A072123 92,100,21,76,21,69,41,116,134,44,76,70,117,80,157,129,87,73,27,157,1,
%U A072123 5,208,27,108,1,203,230,19,112,143,206,258,31,3,146,266,117,213,211,168
%N A072123 Remainder when Fibonacci(n) is divided by prime(n).
%C A072123 For k=0..8, a(10^k) = 1, 26, 55, 5965, 99584, 728618, 2256590, 61329731, 1081853265. - _Zak Seidov_, Dec 23 2014
%H A072123 Alois P. Heinz, <a href="/A072123/b072123.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Zak Seidov)
%F A072123 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.
%e A072123 a(8) = F(8) mod prime(8) = 21 mod 19 = 2.
%p A072123 seq(combinat[fibonacci](n) mod ithprime(n), n=1..1000); # _Robert Israel_, Dec 24 2014
%t A072123 Table[Mod[Fibonacci[n],Prime[n]],{n,70}] (* _Harvey P. Dale_, Jan 25 2011 *)
%o A072123 (Magma) [Fibonacci(n) mod NthPrime(n): n in [1..120]]; // _Vincenzo Librandi_, Nov 19 2015
%o A072123 (PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
%o A072123 a(n)=lift(fibmod(n,prime(n))) \\ _Charles R Greathouse IV_, Jun 19 2017
%Y A072123 Cf. A000040, A000045, A075702 (locations of 0 in this sequence), A121104.
%K A072123 easy,nonn
%O A072123 1,3
%A A072123 _Randy L. Ekl_, Jun 20 2002