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 A051626 Length of the period of decimal representation of 1/n, or 0 if 1/n terminates. 26
 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; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS For any prime number p: if a(p)>0, a(p) divides p-1. - David Spitzer, Jan 09 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Project Euler, Reciprocal cycles: Problem 26 Eric Weisstein's World of Mathematics, Repeating Decimal FORMULA a(n)=A132726(n,1); a(n)=a(A132740(n)); a(A132741(n))=a(A003592(n))=0. - Reinhard Zumkeller, Aug 27 2007 EXAMPLE From M. F. Hasler, Dec 14 2015: (Start) a(1) = a(2) = 0 because 1/1 = 1 and 1/2 = 0.5 have a finite decimal expansion. a(3) = a(6) = a(9) = a(12) = 1 because 1/3 = 0.{3}*, 1/6 = 0.1{6}*, 1/9 = 0.{1}*, 1/12 = 0.08{3}* where the sequence of digits {...}* which repeats indefinitely is of length 1 a(7) = 6 because 1/7 = 0.{142857}* with a period {142857} of length 6. a(17) = 16 because 1/17 = 0.{0588235294117647}* with a period of length 16. a(19) = 18 because 1/19 = 0.{052631578947368421}* with a period {052631578947368421} of length 18. (End) MAPLE A051626 := proc(n) local lpow, mpow ;     if isA003592(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: # R. J. Mathar, Oct 19 2006 MATHEMATICA 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}] (* 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}] (* Ray Chandler, Dec 06 2006 *) Table[Length[RealDigits[1/n][[1, -1]]], {n, 90}] (* Harvey P. Dale, Jul 03 2011 *) PROG (PARI) A051626(n)=if(1

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Last modified December 13 01:24 EST 2018. Contains 318081 sequences. (Running on oeis4.)