login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A224242 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. 0

%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 13:50 EDT 2022. Contains 354071 sequences. (Running on oeis4.)