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A049415 Number of squares (of positive integers) with n digits. 8
3, 6, 22, 68, 217, 683, 2163, 6837, 21623, 68377, 216228, 683772, 2162278, 6837722, 21622777, 68377223, 216227767, 683772233, 2162277661, 6837722339, 21622776602, 68377223398, 216227766017, 683772233983, 2162277660169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) + A180426(n) + A180429(n) + A180347(n) = A052268(n).

Lim_{n->inf.} a(2n)/10^n = 1 - 1/sqrt(10);

lim_{n->inf.} 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))).

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

A049415(n) = A017936(n+1) - A017936(n) = A049416(n+1) - A049416(n).

Cf. A062940.

Sequence in context: A148640 A148641 A148642 * A208939 A209067 A220166

Adjacent sequences:  A049412 A049413 A049414 * A049416 A049417 A049418

KEYWORD

nonn,easy,base

AUTHOR

Ulrich Schimke (ulrschimke(AT)aol.com)

EXTENSIONS

More terms from Dean Hickerson, Jul 10 2001

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)