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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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11
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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
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OFFSET
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1,48
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COMMENTS
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For n > 1: if A023961(n)=9 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
Lim_{n->infinity} a(n)/n = 1/10.
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REFERENCES
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G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
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LINKS
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Table of n, a(n) for n=1..105.
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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: A355478 A097876 A177830 * A156822 A130635 A107609
Adjacent sequences: A111856 A111857 A111858 * 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, Aug 20 2005
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STATUS
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approved
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