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A121341 Number of decimal places before 1/n either recurs or terminates. 5
0, 1, 1, 2, 1, 2, 6, 3, 1, 1, 2, 3, 6, 7, 2, 4, 16, 2, 18, 2, 6, 3, 22, 4, 2, 7, 3, 8, 28, 2, 15, 5, 2, 17, 7, 3, 3, 19, 6, 3, 5, 7, 21, 4, 2, 23, 46, 5, 42, 2, 16, 8, 13, 4, 3, 9, 18, 29, 58, 3, 60, 16, 6, 6, 7, 3, 33, 18, 22, 7, 35, 4, 8, 4, 3, 20, 6, 7, 13, 4, 9, 6, 41, 8, 17, 22, 28, 5, 44, 2, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

In this sequence, the repeating decimals (e.g. 1/7) are treated differently from nonrepeating decimals (e.g. 1/5). If they are treated the same, then a(2)=2, a(4)=3, a(5)=2, a(8)=4, a(10)=2, ... and we obtain A054710. The two sequence differ only for n=2^j 5^k.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

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

EXAMPLE

1/592=0.0016891891891... starts with 4 decimals (0016, zeros counted) and has period 3 (decimals 891) to yield a(592)=4+3=7.

MATHEMATICA

EndingZeros[rep_List] := Module[{cnt=0, i=Length[rep]}, While[rep[[i]]==0, i--; cnt++ ]; cnt]; a[n_Integer] := Module[{lst, e, rep, len, initDigits}, {lst, e}=RealDigits[1/n]; If[VectorQ[lst], len=Length[lst]-e, rep=lst[[ -1]]; initDigits=Length[lst]-1; len=initDigits+Length[rep]-e-EndingZeros[rep]]; len]; Table[a[n], {n, 100}]

CROSSREFS

A007732 is the length of the periods and serves as a lower bound. Cf. A061075.

Sequence in context: A060550 A099206 A269223 * A241737 A174959 A126093

Adjacent sequences:  A121338 A121339 A121340 * A121342 A121343 A121344

KEYWORD

base,easy,nice,nonn

AUTHOR

Anthony C Robin, Aug 29 2006

EXTENSIONS

More terms from T. D. Noe, Aug 30 2006. Additional comments from R. J. Mathar, Aug 30 2006

STATUS

approved

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Last modified December 10 03:42 EST 2016. Contains 278993 sequences.