A224242 - OEIS

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, 4, 24, 44, 112, 480, 1984, 8064, 32512, 130560, 263160, 278828, 340028, 523264, 2095104, 8384512, 25239472, 32490836, 33546240, 134201344, 536838144, 2147418112

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OFFSET

1,2

COMMENTS

A subsequence of A221643: k's such that A221643(k) = A221643(k-1) + 1.

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.

LINKS

Table of n, a(n) for n=1..22.

MATHEMATICA

Select[Range[0, 84*10^5], AllTrue[{Sqrt[BitXor[#^2, (#+1)^2]], Sqrt[BitXor[#^2, (#-1)^2] ]}, IntegerQ]&] (* The program generates the first 16 terms of the sequence. *) (* Harvey P. Dale, Nov 10 2022 *)

PROG

(C)

#include <stdio.h>

#include <math.h>

int main() {

unsigned long long a, i, t;

for (i=0; i < (1L<<32)-1; ++i) {

a = (i*i) ^ ((i+1)*(i+1));

t = sqrt(a);

if (a != t*t) continue;

a = (i*i) ^ ((i-1)*(i-1));

t = sqrt(a);

if (a != t*t) continue;

printf("%llu, ", i);

}

return 0;

}

CROSSREFS

Cf. A221643, A059153.

Sequence in context: A031117 A174178 A139245 * A066770 A080380 A364278

Adjacent sequences: A224239 A224240 A224241 * A224243 A224244 A224245

KEYWORD

nonn,base,less

AUTHOR

Alex Ratushnyak, Apr 01 2013

STATUS

approved