login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121343 a(n) = Fibonacci(n) mod n(n+1)/2. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 12 11:51 EDT 2021. Contains 343821 sequences. (Running on oeis4.)