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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
0, 4, 24, 44, 112, 480, 1984, 8064, 32512, 130560, 263160, 278828, 340028, 523264, 2095104, 8384512, 25239472, 32490836, 33546240, 134201344, 536838144, 2147418112 (list; graph; refs; listen; history; text; internal format)
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.

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 A039935

Adjacent sequences:  A224239 A224240 A224241 * A224243 A224244 A224245

KEYWORD

nonn,base,less

AUTHOR

Alex Ratushnyak, Apr 01 2013

STATUS

approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)