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 A220752 Terms of A220698 that appear in A224218. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 15 20:25 EDT 2024. Contains 375955 sequences. (Running on oeis4.)