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A049068
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Complement of quarter-squares (A002620).
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10
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3, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Numbers k such that floor(sqrt(k)+1/2) does not divide k. - Wesley Ivan Hurt, Dec 01 2020
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LINKS
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FORMULA
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Other identities and observations. For all n >= 1:
G.f.: x/(1-x)^2 + Sum_{k>=0} (x^(1+k^2)*(1+x^k))/(1-x)
= (x*Theta3(x)+ x^(3/4)*Theta2(x))/(2-2*x) + (3-x)*x/(2*(1-x)^2) where Theta3 and Theta2 are Jacobi Theta functions. - Robert Israel, Dec 09 2015
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MAPLE
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MATHEMATICA
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max = 100; Complement[Range[0, max], Table[Quotient[n^2, 4], {n, 0, 2*Sqrt[max]}]] (* Jean-François Alcover, Apr 18 2013 *)
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PROG
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(PARI) {a(n) = if( n<1, 0, n+1 + sqrtint(4*n - 3))} /* Michael Somos, Oct 16 2006 */
(Haskell)
a049068 n = a049068_list !! (n-1)
a049068 = filter ((== 0) . a240025) [0..]
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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