cp's OEIS Frontend

A224511 Roots of squares generated in A221643. That is, S = i^2 XOR (i+1)^2; increment i; if S is a square then square root of S is appended to a(n). Initially i=0. XOR is the binary logical exclusive-or operator.

%I A224511 #14 Feb 01 2025 14:59:53
%S A224511 1,5,3,9,7,13,11,21,17,15,43,45,29,19,41,25,23,59,39,27,35,33,31,85,
%T A224511 37,61,51,53,47,81,79,49,55,121,83,75,57,73,77,67,65,63,71,69,125,89,
%U A224511 87,123,105,107,95,101,163,93,91,99,97,349,243,103,169,109,233,115,119,171
%N A224511 Roots of squares generated in A221643. That is, S = i^2 XOR (i+1)^2; increment i; if S is a square then square root of S is appended to a(n). Initially i=0. XOR is the binary logical exclusive-or operator.
%C A224511 Conjecture: this is a permutation of odd numbers.
%C A224511 b(n) = (a(n)-1)/2  begins: 0, 2, 1, 4, 3, 6, 5, 10, 8, 7, 21, 22, 14, 9, 20, 12, 11, 29, 19, 13, 17.
%o A224511 (Python)
%o A224511 import math
%o A224511 for i in range(1<<16):
%o A224511     s = (i*i) ^ ((i+1)*(i+1))
%o A224511     r = int(math.sqrt(s));
%o A224511     if s == r*r:
%o A224511         print(r, end=', ')
%Y A224511 Cf. A221643, A224515.
%K A224511 nonn,base,less
%O A224511 1,2
%A A224511 _Alex Ratushnyak_, Apr 08 2013