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A175182
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Pisano period length of the 3-Fibonacci numbers A006190.
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3
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1, 3, 2, 6, 12, 6, 16, 12, 6, 12, 8, 6, 52, 48, 12, 24, 16, 6, 40, 12, 16, 24, 22, 12, 60, 156, 18, 48, 28, 12, 64, 48, 8, 48, 48, 6, 76, 120, 52, 12, 28, 48, 42, 24, 12, 66, 96, 24, 112, 60, 16, 156, 26, 18, 24, 48, 40, 84, 24, 12, 30, 192, 48, 96, 156, 24, 136, 48, 22, 48, 144
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OFFSET
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1,2
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COMMENTS
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Period length of the sequence defined by reading A006190 modulo n.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
S. Falcon, A. Plaza, k-Fibonacci sequences modulo m, Chaos, Solit. Fractals 41 (2009) 497-504.
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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 := 3 ; 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[3*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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Cf. A001175, A175181 - A175185.
Sequence in context: A108284 A095011 A188621 * A052616 A091461 A078091
Adjacent sequences: A175179 A175180 A175181 * A175183 A175184 A175185
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KEYWORD
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nonn,easy
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AUTHOR
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R. J. Mathar, Mar 01 2010
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STATUS
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approved
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