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

0,4

Links

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

Formula

A000045(n) modulo A000217(n).

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000045, A023173, A000217, A096535.

Sequence in context: A280198 A175712 A013986 * A321021 A236768 A023439

Adjacent sequences: A121340 A121341 A121342 * A121344 A121345 A121346

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 29 2006

Extensions

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

Status

approved