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A175185
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Pisano period of the 6-Fibonacci numbers A005668.
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12
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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
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OFFSET
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1,2
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COMMENTS
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Period of the sequence defined by reading A005668 modulo n.
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LINKS
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MAPLE
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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) ;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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