A121343 - OEIS

%I #14 Jun 20 2017 02:11:16

%S 0,0,1,2,3,5,8,13,21,34,0,23,66,51,62,10,35,67,19,1,45,89,1,229,168,

%T 275,298,236,319,59,155,125,309,376,407,485,630,628,419,466,615,370,

%U 517,343,663,830,988,1033,168,624,700,746,1167,158,872,1105,609,610,59,1181,0,1,125

%N a(n) = Fibonacci(n) mod n(n+1)/2.

%H Alois P. Heinz, <a href="/A121343/b121343.txt">Table of n, a(n) for n = 0..10000</a>

%F A000045(n) modulo A000217(n).

%e a(11)=23 since Fib(11)=89==23(mod (11*12/2)).

%p a:= proc(n) local r, M, p, m; r, M, p, m:=

%p       <<1|0>, <0|1>>, <<0|1>, <1|1>>, n, n*(n+1)/2;

%p       do if irem(p, 2, 'p')=1 then r:= r.M mod m fi;

%p          if p=0 then break fi; M:= M.M mod m

%p       od; r[1, 2]

%p     end:

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Nov 26 2016

%t f[n_] := If[n == 0, 0, Mod[Fibonacci@n, n(n + 1)/2]]; f /@ Range[0, 62] (* _Robert G. Wilson v_, Aug 31 2006 *)

%t Join[{0},Mod[First[#],Last[#]]&/@With[{nn=70},Thread[{Fibonacci[ Range[ nn]], Accumulate[Range[nn]]}]]] (* _Harvey P. Dale_, May 21 2012 *)

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

%o a(n)=lift(fibmod(n,n*(n+1)/2)) \\ _Charles R Greathouse IV_, Jun 20 2017

%Y Cf. A000045, A023173, A000217, A096535.

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_, Aug 29 2006

%E Edited by _N. J. A. Sloane_, Jul 01 2008 at the suggestion of _R. J. Mathar_