A175184 Pisano period of the 5-Fibonacci numbers, A052918 preceded by 0.

1, 3, 8, 6, 2, 24, 6, 12, 8, 6, 24, 24, 12, 6, 8, 24, 36, 24, 40, 6, 24, 24, 22, 24, 10, 12, 8, 6, 116, 24, 64, 48, 24, 36, 6, 24, 76, 120, 24, 12, 28, 24, 88, 24, 8, 66, 96, 24, 42, 30, 72, 12, 52, 24, 24, 12, 40, 348, 58, 24, 124, 192, 24, 96, 12, 24, 66, 36, 88, 6, 70, 24, 148

Offset

1,2

Comments

Period of the sequence defined by reading A052918 modulo n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Sergio Falcon and Ángel Plaza, k-Fibonacci sequences modulo m, Chaos, Solit. Fractals 41 (2009), 497-504.

Eric Weisstein's World of Mathematics, Pisano period.

Wikipedia, Pisano period.

Maple

F := proc(k, n) option remember; if n <= 1 then n; else k*procname(k, n-1)+procname(k, n-2) ; end if; end proc:
Pper := proc(k, m) local cha, zer, n, fmodm ; cha := [] ; zer := [] ; for n from 0 do fmodm := F(k, n) mod m ; cha := [op(cha), fmodm] ; if fmodm = 0 then zer := [op(zer), n] ; end if; if nops(zer) = 5 then break; end if; end do ; if [op(1..zer[2], cha) ] = [ op(zer[2]+1..zer[3], cha) ] and [op(1..zer[2], cha)] = [ op(zer[3]+1..zer[4], cha) ] and [op(1..zer[2], cha)] = [ op(zer[4]+1..zer[5], cha) ] then return zer[2] ; elif [op(1..zer[3], cha) ] = [ op(zer[3]+1..zer[5], cha) ] then return zer[3] ; else return zer[5] ; end if; end proc:
k := 5 ; seq( Pper(k, m), m=1..80) ;

Mathematica

Table[s = t = Mod[{0, 1}, n]; cnt = 1; While[tmp = Mod[5*t[[2]] + t[[1]], n]; t[[1]] = t[[2]]; t[[2]] = tmp; s!= t, cnt++]; cnt, {n, 100}] (* Vincenzo Librandi, Dec 20 2012, after T. D. Noe *)

Crossrefs

Cf. A001175, A052918, A175181, A175182, A175183, A175185.

Sequence in context: A246727 A081803 A016627 * A019604 A336079 A214726

Adjacent sequences: A175181 A175182 A175183 * A175185 A175186 A175187

Keyword

nonn,easy

Author

R. J. Mathar, Mar 01 2010

Status

approved