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%I
%S 0,4,24,44,112,480,1984,8064,32512,130560,263160,278828,340028,523264,
%T 2095104,8384512,25239472,32490836,33546240,134201344,536838144,
%U 2147418112
%N Numbers k such that k^2 XOR (k+1)^2 is a square, and k^2 XOR (k-1)^2 is a square, where XOR is the bitwise logical XOR operator.
%C A subsequence of A221643: k's such that A221643(k) = A221643(k-1) + 1.
%C A059153 is a subsequence. Terms that are not in A059153: 0, 44, 263160, 278828, 340028, 25239472, 32490836. Conjecture: the subsequence of non-A059153 terms is infinite.
%o (C)
%o #include <stdio.h>
%o #include <math.h>
%o int main() {
%o unsigned long long a, i, t;
%o for (i=0; i < (1L<<32)-1; ++i) {
%o a = (i*i) ^ ((i+1)*(i+1));
%o t = sqrt(a);
%o if (a != t*t) continue;
%o a = (i*i) ^ ((i-1)*(i-1));
%o t = sqrt(a);
%o if (a != t*t) continue;
%o printf("%llu, ", i);
%o }
%o return 0;
%o }
%Y Cf. A221643, A059153.
%K nonn,base,less
%O 1,2
%A _Alex Ratushnyak_, Apr 01 2013
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