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A081318
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Largest factor of 10^a(n)-1 does not produce a decimal fraction period of length n.
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1
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6, 18, 22, 30, 32, 38, 42, 46, 54, 66, 74, 78, 82, 90, 94, 96, 110, 118, 132, 138, 146, 154, 162, 174, 186, 194, 198, 206, 210, 218, 228, 231, 240, 242, 254, 258, 260, 264, 266, 268, 274
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For all but three of the terms through a(41)=274, the reciprocal of the largest prime factor of 10^a(n)-1 is a decimal fraction with a period of a(n)/2. Of the three exceptions, there are two (a(32)=231 and a(38)=264) where the period is a(n)/3, and one (a(19)=132) where the period is a(n)/4. Beyond a(41), terms in the sequence through 300 include 282, 284, 286, 298, and 300 (at each of which the period is a(n)/2), and may also include one or more of 277, 281, 283, and 293 (for each of which the corresponding largest prime factor is not yet known, per the page at the Kamada link). [From Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 27 2010]
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LINKS
| Makoto Kamada, Factorizations of 11...11 (repunit).
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FORMULA
| A061075(a(n)) is not equal to A005422(a(n))
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EXAMPLE
| 30 is in the sequence because the factorization of 10^30-1 is 3^3*7*11*13*31*37*41*211*241*271*_2161_*9091*2906161 2906161 occurs already in 10^15-1=3^3*31*37*41*271*2906161 producing a fraction period of 15, (1/2906161=0.000000344096559000000344096559000000344...) 9091 occurs in 10^10-1=3^2*11*41*271*9091 producing a fraction period of 10. (1/9091=0.0001099989000109998900010999...) 2161 gives the full fraction period 30: 1/2161=0.00462748727440999537251272559000462748727440999537251272559000...
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CROSSREFS
| Cf. A081317.
Sequence in context: A025163 A186889 A022418 * A011775 A015707 A101527
Adjacent sequences: A081315 A081316 A081317 * A081319 A081320 A081321
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KEYWORD
| more,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 18 2003
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EXTENSIONS
| More terms from Hans Havermann (gladhobo(AT)teksavvy.com), May 31 2003
Terms a(31)-a(37) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 19 2010
Terms a(38)-a(41) added, link added, and earlier comment expanded by Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 27 2010
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