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 A175181 Pisano period length of the 2-Fibonacci 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 (list; graph; refs; listen; history; text; internal format)
 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, 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 := 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: A334447 A192034 A209874 * A110003 A035302 A104772 Adjacent sequences: A175178 A175179 A175180 * A175182 A175183 A175184 KEYWORD nonn AUTHOR R. J. Mathar, Mar 01 2010 STATUS approved

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Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)