

A175181


Pisano period length of the 2Fibonacci numbers A000129.


26



1, 2, 8, 4, 12, 8, 6, 8, 24, 12, 24, 8, 28, 6, 24, 16, 16, 24, 40, 12, 24, 24, 22, 8, 60, 28, 72, 12, 20, 24, 30, 32, 24, 16, 12, 24, 76, 40, 56, 24, 10, 24, 88, 24, 24, 22, 46, 16, 42, 60, 16, 28, 108, 72, 24, 24, 40, 20, 40, 24, 124, 30, 24, 64, 84, 24, 136
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OFFSET

1,2


COMMENTS

Period length of the sequence defined by reading A000129 modulo n.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
S. Falcon and A. Plaza, kFibonacci sequences modulo m, Chaos, Solit. Fractals 41 (2009), 497504.
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, n1)+procname(k, n2) ; 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 := 2 ; seq( Pper(k, m), m=1..80) ;


MATHEMATICA

Table[s = t = Mod[{0, 1}, n]; cnt = 1; While[tmp = Mod[2*t[[2]] + t[[1]], n]; t[[1]] = t[[2]]; t[[2]] = tmp; s != t, cnt++]; cnt, {n, 100}] (* T. D. Noe, Jul 09 2012 *)


CROSSREFS

Cf. A000129, A001175, A175182, A175183, A175184, A175185.
Sequence in context: A323986 A192034 A209874 * A110003 A035302 A104772
Adjacent sequences: A175178 A175179 A175180 * A175182 A175183 A175184


KEYWORD

nonn


AUTHOR

R. J. Mathar, Mar 01 2010


STATUS

approved



