A111853 - OEIS

A111853

Number of numbers m <= n such that 3 equals the first digit after decimal point of square root of n in decimal representation.

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

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.

LINKS

Table of n, a(n) for n=1..105.

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 *)

CROSSREFS

Cf. A111850, A111851, A111852, A111854, A111855, A111856, A111857, A111858, A111859, A111893.

Sequence in context: A339183 A135665 A135662 * A111851 A111852 A342676

Adjacent sequences: A111850 A111851 A111852 * A111854 A111855 A111856

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Aug 20 2005

STATUS

approved