cp's OEIS Frontend

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

%I A263737 #16 Jun 28 2022 11:37:31
%S A263737 3,7,11,12,15,19,21,23,24,27,28,31,33,35,39,43,44,47,48,51,55,56,57,
%T A263737 59,60,63,67,69,71,75,76,77,79,83,84,87,88,91,92,93,95,96,99,103,105,
%U A263737 107,108,111,112,115,119,120,123,124,127,129,131,132,133,135,139,140
%N A263737 Nonnegative integers that are the difference of two squares but not the sum of two squares.
%C A263737 Intersection of A022544 (not the sum of two squares) and A042965 (differences of two squares).
%C A263737 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.
%H A263737 Jean-Christophe Hervé, <a href="/A263737/b263737.txt"> Table of n, a(n) for n = 1..5000</a>
%t A263737 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 *)
%o A263737 (Python)
%o A263737 from itertools import count, islice
%o A263737 from sympy import factorint
%o A263737 def A263737_gen(): # generator of terms
%o A263737     return filter(lambda n:n & 3 != 2 and any(p & 3 == 3 and e & 1 for p, e in factorint(n).items()),count(0))
%o A263737 A263737_list = list(islice(A263737_gen(),30)) # _Chai Wah Wu_, Jun 28 2022
%Y A263737 Cf. A001481, A022544, A042965, A016825, A020668, A062316, A097269, A263715.
%K A263737 nonn
%O A263737 1,1
%A A263737 _Jean-Christophe Hervé_, Oct 25 2015