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A111853
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Number of numbers m <= n such that 3 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, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
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OFFSET
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1,19
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COMMENTS
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For n > 1: if A023961(n)=3 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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EXAMPLE
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a(10) = 0, a(100) = 9, a(1000) = 99, a(10000) = 990.
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MATHEMATICA
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fddpQ[n_]:=Module[{a, b}, {a, b}=RealDigits[Surd[n, 2], 10, 10]; a[[b+1]] == 3]; Accumulate[Table[If[fddpQ[n], 1, 0], {n, 110}]] (* Harvey P. Dale, Feb 06 2019 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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