1,2

Period of the sequence defined by reading A001076 modulo n.

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.

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) ;

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 *)

Cf. A001076, A001175, A175181, A175182, A175184, A175185.

Sequence in context: A341741 A074723 A286455 * A189217 A183037 A063077

Adjacent sequences: A175180 A175181 A175182 * A175184 A175185 A175186

nonn,easy

R. J. Mathar, Mar 01 2010

approved