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A036275 The periodic part of the decimal expansion of 1/n. Any initial 0's are to be placed at end of cycle. 17
0, 0, 3, 0, 0, 6, 142857, 0, 1, 0, 90, 3, 769230, 714285, 6, 0, 5882352941176470, 5, 526315789473684210, 0, 476190, 45, 4347826086956521739130, 6, 0, 384615, 370, 571428, 3448275862068965517241379310, 3, 322580645161290, 0, 30, 2941176470588235, 285714, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = 0 iff n = 2^i*5^j (A003592). - Jon Perry, Nov 19 2014

LINKS

Philippe Guglielmetti, Table of n, a(n) for n = 1..1001 (first 500 terms from T. D. Noe)

Index entries for sequences related to decimal expansion of 1/n

EXAMPLE

1/28 = .03571428571428571428571428571428571428571... and digit-cycle is 571428, so a(28)=571428.

MAPLE

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: A036275 := 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 r := (10^lpow-10^mpow)/n ; r := r mod (10^(lpow-mpow)-1) ; while r*10 < 10^(lpow-mpow) do r := 10*r ; od ; RETURN(r) ; fi ; od ; lpow := lpow+1 ; od ; fi ; end: for n from 1 to 60 do printf("%d %d ", n, A036275(n)) ; od ; # 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]];

c[x_] := Which[IntegerQ[l[x]], 0, IntegerQ[f[x]]==False, FromDigits[f[x]], True, FromDigits[l[x]]]; Table[c[i], {i, 1, 36}] (* Hans Havermann, Oct 19 2006 *)

fc[n_] := Block[{q}, q = Last[First[RealDigits[1/n]]]; If[IntegerQ[q], q = {}]; FromDigits[q]]; Table[fc[n], {n, 40}] (* Ray Chandler *)

CROSSREFS

Cf. A007732, A051626, A036275, A002371, A048595, A006883, A007498, A007615, A040017, A051627.

See also A060282, A060283, A060251.

Sequence in context: A110620 A270392 A060284 * A131436 A046765 A046777

Adjacent sequences:  A036272 A036273 A036274 * A036276 A036277 A036278

KEYWORD

base,nonn,easy,nice,changed

AUTHOR

Floor van Lamoen

EXTENSIONS

Corrected and extended by N. J. A. Sloane

Corrected a(92), a(208), a(248), a(328), a(352) and a(488) which missed a trailing zero (see the table). - Philippe Guglielmetti, Jun 20 2017

STATUS

approved

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Last modified June 22 08:02 EDT 2017. Contains 288605 sequences.