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A062940
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Number of squares (including 0) with n digits.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = ceiling(sqrt(10^n)) - ceiling(sqrt(10^(n-1))), n > 1.
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EXAMPLE
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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.
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MAPLE
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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):
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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