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 A111850 Number of numbers m <= n such that 0 equals the first digit after decimal point of square root of n in decimal representation. 11
 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For n > 1: if A023961(n)=0 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1). Lim_{n->infinity} a(n)/n = 1/10. REFERENCES G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178. LINKS EXAMPLE a(10) = 3, a(100) = 15, a(1000) = 118, a(10000) = 1050. MATHEMATICA zd[n_]:=Module[{c=RealDigits[Sqrt[n], 10, 10], f}, f=Last[c]+1; If[First[c][[f]]==0, 1, 0]]; Accumulate[Array[zd, 90]] (* Harvey P. Dale, Feb 01 2012 *) CROSSREFS Cf. A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111890. Sequence in context: A263846 A178786 A000196 * A059396 A108602 A305025 Adjacent sequences:  A111847 A111848 A111849 * A111851 A111852 A111853 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Aug 20 2005 STATUS approved

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Last modified May 7 03:48 EDT 2021. Contains 343636 sequences. (Running on oeis4.)