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A128201
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Union of positive squares and the odd numbers.
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6
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1, 3, 4, 5, 7, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 100, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123
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OFFSET
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1,2
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COMMENTS
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Positive numbers n such that n^((1 + n)/2) is an integer. - Gionata Neri, May 07 2016
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LINKS
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FORMULA
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a(n) = f(n,1,1,2), where f(n,i,m,x) = if i=n then m; else if m+1=x^2 then f(n,i+1,m+1,x); else if m+1>x^2 then f(n,i+1,m+1,x+2); else f(n,i+1,m+2,x).
Set R(n) = 2*n - round(sqrt(2*n)); then a(n) = R(n) + sign(frac(sqrt(R(n)))) * (not(R(n) mod 2)). - Gerald Hillier, Apr 16 2015
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MATHEMATICA
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f[n_] := Block[{s = Range[n]^2, t}, Union[s, Range[1, Last@ s, 2]] // Sort]; f@ 12 (* Michael De Vlieger, Apr 16 2015 *)
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PROG
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(PARI) A128201(n)=!(bittest(n=2*n-round(sqrt(2*n)), 0)||issquare(n))+n \\ Based on Hiliers's formula. - M. F. Hasler, Apr 19 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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