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A108345
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The set N such that each positive integer can be written in the form s^2 + n, s>=0, n in N, in an even number of ways.
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4
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0, 1, 2, 3, 5, 7, 8, 9, 13, 17, 18, 23, 27, 29, 31, 32, 35, 37, 39, 41, 45, 47, 49, 50, 53, 55, 59, 61, 63, 71, 72, 73, 79, 81, 83, 87, 89, 91, 97, 98, 101, 103, 107, 109, 113, 115, 117, 121, 127, 128, 137, 139, 149, 151, 153, 157, 159, 162, 167, 171, 173, 181, 183, 191
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OFFSET
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1,3
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COMMENTS
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This set is conjectured to have zero density. The only even values are the numbers of the form 2n^2. See the paper by Cooper, Eichhorn and O'Bryant for more details. - Franklin T. Adams-Watters, May 16 2006
In a note on arXiv, "Disquisitiones Arithmeticae and online sequence A108345", I show that the upper density is at most 1/16. Furthermore computer evidence presented there suggests that the density is not 0, but 1/32. [From Paul Monsky (monsky(AT)brandeis.edu), Sep 24 2010]
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LINKS
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Table of n, a(n) for n=1..64.
J. N. Cooper, D. Eichhorn and K. O'Bryant, Reciprocals of binary power series
Paul Monsky, Disquisitiones Arithmeticae and online sequence A108345 [From Paul Monsky (monsky(AT)brandeis.edu), Sep 24 2010]
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FORMULA
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The terms are the exponents in the expansion of 1/(Sum_{ n >= 0 } x^(n^2)) read mod 2. - N. J. A. Sloane, Dec 12 2007
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CROSSREFS
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Cf. A132229.
Sequence in context: A187332 A001857 A091532 * A073629 A125716 A171614
Adjacent sequences: A108342 A108343 A108344 * A108346 A108347 A108348
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Jul 01 2005
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EXTENSIONS
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More terms from Franklin T. Adams-Watters, May 16 2006
Changed comment "this set has zero density" to "this set is conjectured to have zero density". - Kevin O'Bryant (obryant(AT)gmail.com), Jul 09 2010
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STATUS
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approved
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