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 A175181 Pisano period length of the 2-Fibonacci numbers A000129. 26

%I

%S 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,

%T 72,12,20,24,30,32,24,16,12,24,76,40,56,24,10,24,88,24,24,22,46,16,42,

%U 60,16,28,108,72,24,24,40,20,40,24,124,30,24,64,84,24,136

%N Pisano period length of the 2-Fibonacci numbers A000129.

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

%H T. D. Noe, <a href="/A175181/b175181.txt">Table of n, a(n) for n = 1..1000</a>

%H S. Falcon and A. Plaza, <a href="http://dx.doi.org/10.1016/j.chaos.2008.02.014">k-Fibonacci sequences modulo m</a>, Chaos, Solit. Fractals 41 (2009), 497-504.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PisanoPeriod.html">Pisano period</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pisano_period">Pisano period</a>.

%p 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:

%p 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:

%p k := 2 ; seq( Pper(k,m),m=1..80) ;

%t 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 *)

%Y Cf. A000129, A001175, A175182, A175183, A175184, A175185.

%K nonn

%O 1,2

%A _R. J. Mathar_, Mar 01 2010

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)