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A217737 a(n) = Fibonacci(n) mod n*(n+1).

%I A217737 #16 Sep 16 2024 12:38:44
%S A217737 1,1,2,3,5,8,13,21,34,55,89,144,51,167,130,171,67,190,1,45,320,1,505,
%T A217737 168,275,649,614,319,59,620,125,837,376,407,485,1296,1331,419,466,
%U A217737 1435,1231,1420,1289,1653,830,2069,2161,1344,1849,1975,746,1167,1589,872,2645,2205
%N A217737 a(n) = Fibonacci(n) mod n*(n+1).
%H A217737 Alois P. Heinz, <a href="/A217737/b217737.txt">Table of n, a(n) for n = 1..10000</a>
%F A217737 A000045(n) modulo A002378(n).
%p A217737 a:= proc(n) local r, M, p, m; r, M, p, m:=
%p A217737       <<1|0>, <0|1>>, <<0|1>, <1|1>>, n, n*(n+1);
%p A217737       do if irem(p, 2, 'p')=1 then r:= r.M mod m fi;
%p A217737          if p=0 then break fi; M:= M.M mod m
%p A217737       od; r[1, 2]
%p A217737     end:
%p A217737 seq(a(n), n=1..100);  # _Alois P. Heinz_, Nov 26 2016
%t A217737 Table[Mod[Fibonacci[n],n(n+1)],{n,60}] (* _Harvey P. Dale_, Oct 02 2017 *)
%o A217737 (Python)
%o A217737 prpr, prev = 0, 1
%o A217737 for i in range(1, 333):
%o A217737     cur = prpr + prev
%o A217737     print(str(prev % (i*(i+1))), end=', ')
%o A217737     prpr, prev = prev, cur
%o A217737 (PARI) a(n)=fibonacci(n)%(n*(n+1)) \\ _Charles R Greathouse IV_, Jun 23 2017
%Y A217737 Cf. A000045, A002708, A121343, A132634, A132636.
%K A217737 nonn,easy
%O A217737 1,3
%A A217737 _Alex Ratushnyak_, Mar 22 2013