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A182213 a(n) = n! mod Fibonacci(n).

%I A182213 #23 Mar 13 2023 11:17:59
%S A182213 0,0,0,0,0,0,9,0,32,10,33,0,37,273,80,840,1116,816,404,1485,1742,7854,
%T A182213 27833,0,49100,37681,66606,85839,222482,656920,1335931,417165,362268,
%U A182213 3309347,1266460,976752,20352231,19601527,4303068,8848455,136897669,254107048
%N A182213 a(n) = n! mod Fibonacci(n).
%H A182213 Vincenzo Librandi, <a href="/A182213/b182213.txt">Table of n, a(n) for n = 1..1000</a>
%F A182213 a(n) = A000142(n) mod A000045(n), n>0.
%F A182213 a(n) = n! mod fibonacci(n), n>0.
%e A182213 a(6) = 720 mod 8 = 0, a(7)= 5040 mod 13 = 9.
%t A182213 Table[Mod[n!, Fibonacci[n]], {n, 50}] (* _T. D. Noe_, Apr 19 2012 *)
%o A182213 (Python)
%o A182213 prpr = 0
%o A182213 prev = 1
%o A182213 fa = 1
%o A182213 for i in range(2,50):
%o A182213     print(fa % prev, end=',')
%o A182213     fa *= i
%o A182213     current = prev + prpr
%o A182213     prpr = prev
%o A182213     prev = current
%o A182213 (PARI) a(n) = n!%fibonacci(n); \\ _Bill McEachen_, Feb 03 2014
%o A182213 (Magma) [Factorial(n) mod Fibonacci(n): n in [1..50]]; // _Vincenzo Librandi_, Feb 04 2014
%Y A182213 Cf. A000045, A000142, A182212.
%K A182213 nonn,easy
%O A182213 1,7
%A A182213 _Alex Ratushnyak_, Apr 19 2012