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A111851
Number of numbers m <= n such that 1 equals the first digit after decimal point of square root of n in decimal representation.
12
0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11
OFFSET
1,17
REFERENCES
G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
FORMULA
For n > 1: if A023961(n)=1 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
Limit_{n->oo} a(n)/n = 1/10.
EXAMPLE
a(10) = 1, a(100) = 9, a(1000) = 99, a(10000) = 990.
MATHEMATICA
Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 1] &, 100]] (* Paolo Xausa, May 17 2024 *)
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Aug 20 2005
STATUS
approved