A175183 Pisano period of the 4-Fibonacci numbers A001076.

1, 2, 8, 2, 20, 8, 16, 4, 8, 20, 10, 8, 28, 16, 40, 8, 12, 8, 6, 20, 16, 10, 16, 8, 100, 28, 24, 16, 14, 40, 10, 16, 40, 12, 80, 8, 76, 6, 56, 20, 40, 16, 88, 10, 40, 16, 32, 8, 112, 100, 24, 28, 36, 24, 20, 16, 24, 14, 58, 40, 20, 10, 16, 32, 140, 40, 136, 12, 16, 80, 70, 8, 148, 76

Offset

1,2

Comments

Period of the sequence defined by reading A001076 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 := 4 ; seq( Pper(k, m), m=1..80) ;

Mathematica

Table[s = t = Mod[{0, 1}, n]; cnt=1; While[tmp = Mod[4*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. A001076, A001175, A175181, A175182, A175184, A175185.

Sequence in context: A341741 A074723 A286455 * A189217 A183037 A063077

Adjacent sequences: A175180 A175181 A175182 * A175184 A175185 A175186

Keyword

nonn,easy

Author

R. J. Mathar, Mar 01 2010

Status

approved