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A087279
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Nonnegative numbers such that distance to nearest positive square equals exactly 1.
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1
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0, 2, 3, 5, 8, 10, 15, 17, 24, 26, 35, 37, 48, 50, 63, 65, 80, 82, 99, 101, 120, 122, 143, 145, 168, 170, 195, 197, 224, 226, 255, 257, 288, 290, 323, 325, 360, 362, 399, 401, 440, 442, 483, 485, 528, 530, 575, 577, 624, 626, 675, 677, 728, 730, 783, 785, 840
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Union of A005563 and A002522\{1}: a(2*k+1) = (k+1)^2 - 1 = A005563(k); a(2*k) = k^2 + 1 = A002522(k); positive square + 1 or positive square - 1.
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FORMULA
| a(1) = 0; a(2*k+1) = a(2*k) + 2*k-1; a(2*k) = a(2*k-1) + 2.
a(n-1) = floor((n+1)/2)^2+(-1)^(n mod 2).
G.f.: x^2*(2+x-2*x^2+x^3)/((1+x)^2*(1-x)^3). a(n) = (2*n*(n+1)-(2*n-7)*(-1)^n+1)/8 - Bruno Berselli, Apr 21 2011
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PROG
| (MAGMA) &cat[[n^2-1, n^2+1]: n in [1..30]]; // Bruno Berselli, Apr 21 2011
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CROSSREFS
| Cf. A000290, A004526, A000035, A087278.
Sequence in context: A094568 A183871 A022955 * A084907 A158724 A181100
Adjacent sequences: A087276 A087277 A087278 * A087280 A087281 A087282
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 28 2003
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EXTENSIONS
| Franklin T. Adams-Watters pointed out on Jun 26 2007 that there were problems with the first couple of terems. I have made some changes, so now the definition matches the sequence. But some of the comments may need further minor adjustments. - N. J. A. Sloane (njas(AT)research.att.com), Jun 01 2008
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