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A062940 Number of squares (including 0) with n digits.

%I A062940 #22 Jun 28 2018 04:45:46
%S A062940 4,6,22,68,217,683,2163,6837,21623,68377,216228,683772,2162278,
%T A062940 6837722,21622777,68377223,216227767,683772233,2162277661,6837722339,
%U A062940 21622776602,68377223398,216227766017,683772233983,2162277660169
%N A062940 Number of squares (including 0) with n digits.
%C A062940 Sum of first 2n terms = 10^n. - _Zak Seidov_, Aug 05 2006
%C A062940 a(n)/a(n-1) ~ 10^(1/2). For the sequence giving the number of members of the sequence a(k)=k^r with n digits we have a(n)/a(n-1) ~ 10^(1/r). - _Ctibor O. Zizka_, Mar 09 2008
%H A062940 Harry J. Smith, <a href="/A062940/b062940.txt">Table of n, a(n) for n = 1..200</a>
%F A062940 a(n) = ceiling(sqrt(10^n)) - ceiling(sqrt(10^(n-1))), n > 1.
%F A062940 a(n) = A017934(n) - A017934(n-1) - (-1)^n, n >= 2. - _R. J. Mathar_, Mar 17 2008
%e A062940 a(1)=4 because there are 4 one-digit squares: 0,1,4,9. - _Zak Seidov_, Aug 05 2006
%e A062940 a(2)=6 because there are 6 two-digit squares: 16,25,36,49,64,81. - _Zak Seidov_, Aug 05 2006
%e A062940 22 squares (100=10^2, 121=11^2, ..., 961=31^2) have 3 digits, hence a(3)=22.
%p A062940 r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:
%p A062940 a:= n-> r(10^n, 2) -r(10^(n-1), 2) +`if`(n=1, 1, 0):
%p A062940 seq(a(n), n=1..40);  # _Alois P. Heinz_, Sep 12 2012
%o A062940 (PARI) je=[4]; for(n=2, 45, je=concat(je, ceil(sqrt(10^n))-ceil(sqrt(10^(n-1))))); je
%o A062940 (PARI) { default(realprecision, 200); for (n=1, 200, b=ceil(10^(n/2)); if (n>1, a=b - c, a=4); c=b; write("b062940.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 14 2009
%Y A062940 A variant of A049415. A049415(n) = A017936(n+1) - A017936(n) = A049416(n+1) - A049416(n). Cf. A000290, A062941.
%Y A062940 Column k=2 of A216653.
%K A062940 nonn,easy,base
%O A062940 1,1
%A A062940 _Amarnath Murthy_, Jul 07 2001
%E A062940 Corrected and extended by _Dean Hickerson_ and _Jason Earls_, Jul 10 2001
%E A062940 Edited by _R. J. Mathar_, Aug 07 2008