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Search: id:A051626
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| A051626 |
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Period of decimal representation of 1/n, or 0 if 1/n terminates. |
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+0
11
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| 0, 0, 1, 0, 0, 1, 6, 0, 1, 0, 2, 1, 6, 6, 1, 0, 16, 1, 18, 0, 6, 2, 22, 1, 0, 6, 3, 6, 28, 1, 15, 0, 2, 16, 6, 1, 3, 18, 6, 0, 5, 6, 21, 2, 1, 22, 46, 1, 42, 0, 16, 6, 13, 3, 2, 6, 18, 28, 58, 1, 60, 15, 6, 0, 6, 2, 33, 16, 22, 6, 35, 1, 8, 3, 1, 18, 6, 6, 13, 0, 9, 5, 41, 6, 16, 21, 28, 2, 44, 1
(list; graph; listen)
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OFFSET
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1,7
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LINKS
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Eric Weisstein's World of Mathematics, Repeating Decimal
Index entries for sequences related to decimal expansion of 1/n
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FORMULA
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a(n)=A132726(n,1); a(n)=a(A132740(n)); a(A132741(n))=a(A003592(n))=0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 27 2007
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MAPLE
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isCycl := proc(n) local ifa, i ; if n <= 2 then RETURN(false) ; fi ; ifa := ifactors(n)[2] ; for i from 1 to nops(ifa) do if op(1, op(i, ifa)) <> 2 and op(1, op(i, ifa)) <> 5 then RETURN(true) ; fi ; od ; RETURN(false) ; end: A051626 := proc(n) local ifa, sh, lpow, mpow, r ; if not isCycl(n) then RETURN(0) ; else lpow:=1 ; while true do for mpow from lpow-1 to 0 by -1 do if (10^lpow-10^mpow) mod n =0 then RETURN(lpow-mpow) ; fi ; od ; lpow := lpow+1 ; od ; fi ; end: for n from 1 to 600 do printf("%d %d ", n, A051626(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 19 2006
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MATHEMATICA
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r[x_]:=RealDigits[1/x]; w[x_]:=First[r[x]]; f[x_]:=First[w[x]]; l[x_]:=Last[w[x]]; z[x_]:=Last[r[x]];
d[x_] := Which[IntegerQ[l[x]], 0, IntegerQ[f[x]]==False, Length[f[x]], True, Length[l[x]]]; Table[d[i], {i, 1, 90}] (from Hans Havermann, Oct 19 2006)
fd[n_] := Block[{q}, q = Last[First[RealDigits[1/n]]]; If[IntegerQ[q], q = {}]; Length[q]]; Table[fd[n], {n, 100}] (*Chandler*)
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CROSSREFS
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Essentially same as A007732. Cf. A048595, A006883, A036275, A114205, A114206.
Sequence in context: A060297 A137378 A084680 this_sequence A137785 A134899 A076413
Adjacent sequences: A051623 A051624 A051625 this_sequence A051627 A051628 A051629
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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J. Lowell (jhbubby(AT)avana.net)
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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