cp's OEIS Frontend

A220752 Terms of A220698 that appear in A224218.

%I A220752 #14 Apr 27 2013 13:48:46
%S A220752 3854,3854,3035,3035,3035,3035,3854,4644,4644,4644,4644,4644,3854,
%T A220752 15846,4644,4644,4644,4644,4644,22918,15846,15846,10225,10225,10225,
%U A220752 10225,15846,22918,15846,13364,13364,13364,13364,10225,10225,10225,10225,15846,13364,13364,22918,45012
%N A220752 Terms of A220698 that appear in A224218.
%C A220752 Terms of A220698 excluding terms that do not appear in A224218.
%C A220752 Indices of XOR-positive triangular numbers such that the generated triangular number is also XOR-positive (definition: triangular(i) is XOR-positive if triangular(i) XOR triangular(i+1) = triangular(k) for some k). XOR is the bitwise logical exclusive-or operator.
%C A220752 Conjecture: the sequence is infinite.
%C A220752 The subsequence with only odd terms begins: 3035, 3035, 3035, 3035, 10225, 10225, 10225, 10225, 10225, 10225, 10225, 10225, 171449, 171449, 236985, 171449, 339249.
%o A220752 (C)
%o A220752 #include <stdio.h>
%o A220752 typedef unsigned long long U64;
%o A220752 U64 rootTriangular(U64 a) {
%o A220752     U64 sr = 1L<<32, s, b;
%o A220752     if (a < (sr/2)*(sr+1)) {
%o A220752           sr>>=1;
%o A220752           while (a < sr*(sr+1)/2)  sr>>=1;
%o A220752     }
%o A220752     for (b = sr>>1; b; b>>=1) {
%o A220752             s = sr+b;
%o A220752             if (a >= s*(s+1)/2)  sr = s;
%o A220752     }
%o A220752     return sr;
%o A220752 }
%o A220752 int main() {
%o A220752   U64 a, n, r, t;
%o A220752   for (n=0; n < (1L<<32)-1; n++) {
%o A220752     a = (n*(n+1)/2) ^ ((n+1)*(n+2)/2);
%o A220752     t = rootTriangular(a);
%o A220752     if (a == t*(t+1)/2) {
%o A220752         a ^= (t+1)*(t+2)/2;
%o A220752         r = rootTriangular(a);
%o A220752         if (a == r*(r+1)/2)  printf("%llu, ", t);
%o A220752     }
%o A220752   }
%o A220752 }
%Y A220752 Cf. A000217, A224218, A220698.
%K A220752 nonn,base
%O A220752 1,1
%A A220752 _Alex Ratushnyak_, Apr 13 2013