A121343 a(n) = Fibonacci(n) mod n(n+1)/2.

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, 275, 298, 236, 319, 59, 155, 125, 309, 376, 407, 485, 630, 628, 419, 466, 615, 370, 517, 343, 663, 830, 988, 1033, 168, 624, 700, 746, 1167, 158, 872, 1105, 609, 610, 59, 1181, 0, 1, 125

Offset: 0

Author

N. J. A. Sloane, Aug 29 2006

Keywords

• nonn
• easy

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000045, A023173, A000217, A096535.

Programs

Maple

a:= proc(n) local r, M, p, m; r, M, p, m:=
      <<1|0>, <0|1>>, <<0|1>, <1|1>>, n, n*(n+1)/2;
      do if irem(p, 2, 'p')=1 then r:= r.M mod m fi;
         if p=0 then break fi; M:= M.M mod m
      od; r[1, 2]
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Nov 26 2016

Mathematica

f[n_] := If[n == 0, 0, Mod[Fibonacci@n, n(n + 1)/2]]; f /@ Range[0, 62] (* Robert G. Wilson v, Aug 31 2006 *)
Join[{0},Mod[First[#],Last[#]]&/@With[{nn=70},Thread[{Fibonacci[ Range[ nn]], Accumulate[Range[nn]]}]]] (* Harvey P. Dale, May 21 2012 *)

PARI

fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
a(n)=lift(fibmod(n,n*(n+1)/2)) \\ Charles R Greathouse IV, Jun 20 2017

Formula

A000045(n) modulo A000217(n).

Extensions

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar