A263737 Nonnegative integers that are the difference of two squares but not the sum of two squares.

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

Offset

1,1

Comments

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.

Links

Jean-Christophe Hervé, Table of n, a(n) for n = 1..5000

Mathematica

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 *)

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A263737_gen(): # generator of terms
    return filter(lambda n:n & 3 != 2 and any(p & 3 == 3 and e & 1 for p, e in factorint(n).items()), count(0))
A263737_list = list(islice(A263737_gen(), 30)) # Chai Wah Wu, Jun 28 2022

Crossrefs

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

Keyword

nonn

Author

Jean-Christophe Hervé, Oct 25 2015

Status

approved