A220752 - OEIS

%I #14 Apr 27 2013 13:48:46

%S 3854,3854,3035,3035,3035,3035,3854,4644,4644,4644,4644,4644,3854,

%T 15846,4644,4644,4644,4644,4644,22918,15846,15846,10225,10225,10225,

%U 10225,15846,22918,15846,13364,13364,13364,13364,10225,10225,10225,10225,15846,13364,13364,22918,45012

%N Terms of A220698 that appear in A224218.

%C Terms of A220698 excluding terms that do not appear in A224218.

%C 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 Conjecture: the sequence is infinite.

%C 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 (C)

%o #include <stdio.h>

%o typedef unsigned long long U64;

%o U64 rootTriangular(U64 a) {

%o     U64 sr = 1L<<32, s, b;

%o     if (a < (sr/2)*(sr+1)) {

%o           sr>>=1;

%o           while (a < sr*(sr+1)/2)  sr>>=1;

%o     }

%o     for (b = sr>>1; b; b>>=1) {

%o             s = sr+b;

%o             if (a >= s*(s+1)/2)  sr = s;

%o     }

%o     return sr;

%o }

%o int main() {

%o   U64 a, n, r, t;

%o   for (n=0; n < (1L<<32)-1; n++) {

%o     a = (n*(n+1)/2) ^ ((n+1)*(n+2)/2);

%o     t = rootTriangular(a);

%o     if (a == t*(t+1)/2) {

%o         a ^= (t+1)*(t+2)/2;

%o         r = rootTriangular(a);

%o         if (a == r*(r+1)/2)  printf("%llu, ", t);

%o     }

%o   }

%o }

%Y Cf. A000217, A224218, A220698.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Apr 13 2013