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 A175185 Pisano period length of the 6-Fibonacci numbers A005668. 12
 1, 2, 2, 4, 20, 2, 16, 8, 6, 20, 24, 4, 6, 16, 20, 16, 36, 6, 8, 20, 16, 24, 48, 8, 100, 6, 18, 16, 60, 20, 30, 32, 24, 36, 80, 12, 12, 8, 6, 40, 40, 16, 42, 24, 60, 48, 96, 16, 112, 100, 36, 12, 26, 18, 120, 16, 8, 60, 40, 20, 124, 30, 48, 64, 60, 24, 22, 36, 48, 80, 70, 24, 148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Period length of the sequence defined by reading A005668 modulo n. LINKS Vincenzo Librandi, 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 := 6 ; seq( Pper(k, m), m=1..80) ; MATHEMATICA Table[s = t = Mod[{0, 1}, n]; cnt = 1; While[tmp = Mod[6*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. A001175, A175181, A175182, A175183, A175184. Sequence in context: A052628 A006853 A120417 * A257610 A062267 A128501 Adjacent sequences:  A175182 A175183 A175184 * A175186 A175187 A175188 KEYWORD nonn,easy AUTHOR R. J. Mathar, Mar 01 2010 STATUS approved

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Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)