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Search: id:A121341
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| A121341 |
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Number of decimal places before 1/n either recurs or terminates. |
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+0
4
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for sequences related to decimal expansion of 1/n
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EXAMPLE
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1/592=0.0016891891891... starts with 4 decimals (0016, zeros counted) and has period 3 (decimals 891) to yield a(592)=4+3=7.
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MATHEMATICA
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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}]
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CROSSREFS
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A007732 is the length of the periods and serves as a lower bound. Cf. A061075.
Sequence in context: A053448 A060550 A099206 this_sequence A126093 A065279 A069627
Adjacent sequences: A121338 A121339 A121340 this_sequence A121342 A121343 A121344
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KEYWORD
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base,easy,nice,nonn
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AUTHOR
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Anthony C Robin (anthony_robin(AT)hotmail.com), Aug 29 2006
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Aug 30 2006. Additional comments from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 30 2006
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