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A062940
Number of squares (including 0) with n digits.
5
4, 6, 22, 68, 217, 683, 2163, 6837, 21623, 68377, 216228, 683772, 2162278, 6837722, 21622777, 68377223, 216227767, 683772233, 2162277661, 6837722339, 21622776602, 68377223398, 216227766017, 683772233983, 2162277660169
OFFSET
1,1
COMMENTS
Sum of first 2n terms = 10^n. - Zak Seidov, Aug 05 2006
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
LINKS
FORMULA
a(n) = ceiling(sqrt(10^n)) - ceiling(sqrt(10^(n-1))), n > 1.
a(n) = A017934(n) - A017934(n-1) - (-1)^n, n >= 2. - R. J. Mathar, Mar 17 2008
EXAMPLE
a(1)=4 because there are 4 one-digit squares: 0,1,4,9. - Zak Seidov, Aug 05 2006
a(2)=6 because there are 6 two-digit squares: 16,25,36,49,64,81. - Zak Seidov, Aug 05 2006
22 squares (100=10^2, 121=11^2, ..., 961=31^2) have 3 digits, hence a(3)=22.
MAPLE
r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:
a:= n-> r(10^n, 2) -r(10^(n-1), 2) +`if`(n=1, 1, 0):
seq(a(n), n=1..40); # Alois P. Heinz, Sep 12 2012
PROG
(PARI) je=[4]; for(n=2, 45, je=concat(je, ceil(sqrt(10^n))-ceil(sqrt(10^(n-1))))); je
(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
CROSSREFS
A variant of A049415. A049415(n) = A017936(n+1) - A017936(n) = A049416(n+1) - A049416(n). Cf. A000290, A062941.
Column k=2 of A216653.
Sequence in context: A289385 A151519 A061595 * A061596 A061597 A075813
KEYWORD
nonn,easy,base
AUTHOR
Amarnath Murthy, Jul 07 2001
EXTENSIONS
Corrected and extended by Dean Hickerson and Jason Earls, Jul 10 2001
Edited by R. J. Mathar, Aug 07 2008
STATUS
approved