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Search: id:A111859
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| A111859 |
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Number of numbers m <= n such that 9 equals the first digit after decimal point of square root of n in decimal representation. |
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+0
12
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5
(list; graph; listen)
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OFFSET
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1,48
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COMMENT
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For n>1: if A023961(n)=9 then a(n)=a(n-1)+1 else a(n)=a(n-1).
a(n)/n --> 1/10.
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REFERENCES
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G. Polya and G. Szego, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
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EXAMPLE
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a(10) = 0, a(100) = 5, a(1000) = 81, a(10000) = 950.
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CROSSREFS
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Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111899.
Sequence in context: A046042 A071841 A097876 this_sequence A156822 A107609 A135660
Adjacent sequences: A111856 A111857 A111858 this_sequence A111860 A111861 A111862
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2005
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