OFFSET
1,1
COMMENTS
Lim_{n->infinity} a(2n)/10^n = 1 - 1/sqrt(10);
lim_{n->infinity} a(2n-1)/10^n = 1/sqrt(10) - 1/10. - Robert G. Wilson v, Aug 29 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = ceiling(sqrt(10^n)) - ceiling(sqrt(10^(n-1))).
From Jon E. Schoenfield, Nov 30 2019: (Start)
a(2n) = floor(10^n * (1 - 1/sqrt(10))), so each even-indexed term a(2n) is given by the first n digits (after the decimal point) of 1 - 1/sqrt(10) = 0.68377223398316...;
a(2n-1) = ceiling(10^n * (1/sqrt(10) - 1/10)), so each odd-indexed term a(2n-1) is given by the first n digits (after the decimal point) of 1/sqrt(10) - 1/10 = 0.21622776601683..., plus 1. (End)
EXAMPLE
22 squares (100=10^2, 121=11^2, ...., 961=31^2) have 3 digits, hence a(3)=22.
MATHEMATICA
f[n_] := Ceiling[Sqrt[10^n - 1]] - Ceiling[Sqrt[10^(n - 1)]]; f[1] = 3; Array[f, 24] (* Robert G. Wilson v, Aug 29 2012 *)
PROG
(Magma) [Ceiling(Sqrt(10^n))-Ceiling(Sqrt(10^(n-1))) : n in [1..30]]; // Vincenzo Librandi, Oct 01 2011
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
EXTENSIONS
More terms from Dean Hickerson, Jul 10 2001
STATUS
approved