

A263715


Nonnegative integers that are the sum or difference of two squares.


5



0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 80
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OFFSET

1,3


COMMENTS

Contains all integers that are not equal to 2 (mod 4) (they are of the form y^2  x^2) and those of the form 4k+2 = 2*(2k+1) with the odd number 2k+1 equal to the sum of two squares (A057653).


LINKS

JeanChristophe Hervé, Table of n, a(n) for n = 1..10000


FORMULA

Union of A001481 (sums of two squares) and A042965 (differences of two squares).
Union of A042965 and 2*A057653 = A097269, with intersection of A042965 and A097269 = {}.
Union of A020668 (x^2+y^2 and a^2b^2), A097269 (x^2+y^2, not a^2b^2) and A263737 (not x^2+y^2, a^2b^2).


EXAMPLE

2 = 1^2 + 1^2, 3 = 2^2  1^2, 4 = 2^2 + 0^2, 5 = 2^2 + 1^2 = 3^2  2^2.


MATHEMATICA

r[n_] := Reduce[n == x^2 + y^2, {x, y}, Integers]  Reduce[0 <= y <= x && n == x^2  y^2, {x, y}, Integers]; Reap[Do[If[r[n] =!= False, Sow[n]], {n, 0, 80}]][[2, 1]] (* JeanFrançois Alcover, Oct 25 2015 *)


CROSSREFS

Cf. A001481, A057653, A097269, A042965, A020668, A263737.
Cf. A062316 (complement), A079298.
Sequence in context: A088451 A047595 A079298 * A023055 A230872 A247832
Adjacent sequences: A263712 A263713 A263714 * A263716 A263717 A263718


KEYWORD

nonn


AUTHOR

JeanChristophe Hervé, Oct 24 2015


STATUS

approved



