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A111853
Number of numbers m <= n such that 3 equals the first digit after decimal point of square root of n in decimal representation.
11
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
OFFSET
1,19
COMMENTS
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.
REFERENCES
G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
EXAMPLE
a(10) = 0, a(100) = 9, a(1000) = 99, a(10000) = 990.
MATHEMATICA
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 *)
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Aug 20 2005
STATUS
approved