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0, 9, 1089, 110889, 11108889, 1111088889, 111110888889, 11111108888889, 1111111088888889, 111111110888888889, 11111111108888888889, 1111111111088888888889, 111111111110888888888889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A transformation of the Wonderful Demlo numbers (A002477).
a(n) = A002283(n)*A002275(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
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LINKS
| G. Villemin, Variations sur les carres
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FORMULA
| a(n) = A002277(n)^2 = (3 * A002275(n) )^2 = 9 * (A002275(n) )^2
a(n) = {111111... (2n times)} - 2*{ 111... (n times)} a(n) = A000042(2n) - 2*A000042(n). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 21 2003
a(n)={333... (n times)}^2 ={111...(n times)}{000... (n times)} - {111... (n times)}. For example, 333^2 = 111000 - 111 = 110889. [From Kyle D. Balliet (kdballie(AT)bloomu.edu), Mar 07 2009]
n>0: a(n) = (A002275(n-1)*10^n + A002282(n-1))*10 + 9. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
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EXAMPLE
| a(2) = 33^2 = 1089.
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010: (Start)
n=1: ...................... 9 = 9 * 1;
n=2: ................... 1089 = 99 * 11;
n=3: ................. 110889 = 999 * 111;
n=4: ............... 11108889 = 9999 * 1111;
n=5: ............. 1111088889 = 99999 * 11111;
n=6: ........... 111110888889 = 999999 * 111111;
n=7: ......... 11111108888889 = 9999999 * 1111111;
n=8: ....... 1111111088888889 = 99999999 * 11111111;
n=9: ..... 111111110888888889 = 999999999 * 111111111. (End)
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CROSSREFS
| Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417, A002283.
Cf. A178630, A178631, A178632, A178633, A178634, A178635, A059988. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
Sequence in context: A054344 A048912 A036411 * A174253 A084149 A202981
Adjacent sequences: A075409 A075410 A075411 * A075413 A075414 A075415
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KEYWORD
| easy,nonn
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AUTHOR
| Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002
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