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0, 81, 9801, 998001, 99980001, 9999800001, 999998000001, 99999980000001, 9999999800000001, 999999998000000001, 99999999980000000001, 9999999999800000000001, 999999999998000000000001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Comment from James D. Klein, Feb 05 2012: (Start)
The periods of the reciprocals of a(n) are the consecutive integers from 0 to 10^n-1, omitting the one integer 10^n-2, right-justified in field widths of size n. E.g.:
1/81 = 0.012345679...
1/9801 = 0.000102030405060708091011...9799000102...
1/998001 = 0.000001002003004005...997999000001002... (End)
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REFERENCES
| Walther Lietzmann, Lustiges und Merkwuerdiges von Zahlen und Formen, (F. Hirt, Breslau 1921-43), p. 149. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
| a(n) = 81*A002477(n) = A002283(n)^2 = (9*A002275(n))^2.
a(n)={999... (n times)}^2={999... (n times),000... (n times)} - {999... (n times)}. For example, 999^2=999000-999=998001. [From Kyle D. Balliet (kdballie(AT)bloomu.edu), Mar 07 2009]
n>0: a(n) = (A002283(n-1)*10 + 8) * 10^(n-1) + 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
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EXAMPLE
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010: (Start)
n=1: ..................... 81 = 9^2;
n=2: ................... 9801 = 99^2;
n=3: ................. 998001 = 999^2;
n=4: ............... 99980001 = 9999^2;
n=5: ............. 9999800001 = 99999^2;
n=6: ........... 999998000001 = 999999^2;
n=7: ......... 99999980000001 = 9999999^2;
n=8: ....... 9999999800000001 = 99999999^2;
n=9: ..... 999999998000000001 = 999999999^2. (End)
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PROG
| (PARI) { for (n=0, 200, write("b059988.txt", n, " ", (10^n - 1)^2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 01 2009]
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CROSSREFS
| Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417.
Cf. A178630, A178631, A178632, A178633, A178634, A178635, A059988. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
Sequence in context: A184337 A034993 A093281 * A017020 A185847 A058422
Adjacent sequences: A059985 A059986 A059987 * A059989 A059990 A059991
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 07 2001
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