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A263737
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Nonnegative integers that are the difference of two squares but not the sum of two squares.
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3
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3, 7, 11, 12, 15, 19, 21, 23, 24, 27, 28, 31, 33, 35, 39, 43, 44, 47, 48, 51, 55, 56, 57, 59, 60, 63, 67, 69, 71, 75, 76, 77, 79, 83, 84, 87, 88, 91, 92, 93, 95, 96, 99, 103, 105, 107, 108, 111, 112, 115, 119, 120, 123, 124, 127, 129, 131, 132, 133, 135, 139, 140
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OFFSET
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1,1
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COMMENTS
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Intersection of A022544 (not the sum of two squares) and A042965 (differences of two squares).
The sequence contains all 4k + 3 and no 4k + 2 integers, and some 4k (4*A022544) and 4k+1 (A084109) integers. First differences are thus 1, 2, 3 or 4, each occurring infinitely often.
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LINKS
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Jean-Christophe Hervé, Table of n, a(n) for n = 1..5000
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MATHEMATICA
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rs[n_] := Reduce[n == x^2 + y^2, {x, y}, Integers]; rd[n_] := Reduce[0 <= y <= x && n == x^2 - y^2, {x, y}, Integers]; Reap[Do[If[rs[n] == False && rd[n] =!= False, Sow[n]], {n, 0, 140}]][[2, 1]] (* Jean-François Alcover, Oct 26 2015 *)
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CROSSREFS
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Cf. A001481, A022544, A042965, A016825, A020668, A062316, A097269, A263715.
Sequence in context: A076184 A310191 A135137 * A055050 A096346 A104534
Adjacent sequences: A263734 A263735 A263736 * A263738 A263739 A263740
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KEYWORD
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nonn
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AUTHOR
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Jean-Christophe Hervé, Oct 25 2015
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STATUS
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approved
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