A220752 Terms of A220698 that appear in A224218.

3854, 3854, 3035, 3035, 3035, 3035, 3854, 4644, 4644, 4644, 4644, 4644, 3854, 15846, 4644, 4644, 4644, 4644, 4644, 22918, 15846, 15846, 10225, 10225, 10225, 10225, 15846, 22918, 15846, 13364, 13364, 13364, 13364, 10225, 10225, 10225, 10225, 15846, 13364, 13364, 22918, 45012

Offset

1,1

Comments

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

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.

Conjecture: the sequence is infinite.

The subsequence with only odd terms begins: 3035, 3035, 3035, 3035, 10225, 10225, 10225, 10225, 10225, 10225, 10225, 10225, 171449, 171449, 236985, 171449, 339249.

Links

Table of n, a(n) for n=1..42.

Prog

(C)
#include <stdio.h>
typedef unsigned long long U64;
U64 rootTriangular(U64 a) {
    U64 sr = 1L<<32, s, b;
    if (a < (sr/2)*(sr+1)) {
          sr>>=1;
          while (a < sr*(sr+1)/2)  sr>>=1;
    }
    for (b = sr>>1; b; b>>=1) {
            s = sr+b;
            if (a >= s*(s+1)/2)  sr = s;
    }
    return sr;
}
int main() {
  U64 a, n, r, t;
  for (n=0; n < (1L<<32)-1; n++) {
    a = (n*(n+1)/2) ^ ((n+1)*(n+2)/2);
    t = rootTriangular(a);
    if (a == t*(t+1)/2) {
        a ^= (t+1)*(t+2)/2;
        r = rootTriangular(a);
        if (a == r*(r+1)/2)  printf("%llu, ", t);
    }
  }
}

Crossrefs

Cf. A000217, A224218, A220698.

Sequence in context: A015069 A015070 A031629 * A257780 A068267 A205409

Adjacent sequences: A220749 A220750 A220751 * A220753 A220754 A220755

Keyword

nonn,base

Author

Alex Ratushnyak, Apr 13 2013

Status

approved