A340379 Number of 2-digits in the ternary representation of A048673(n).

0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 1, 0, 1, 0, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 2, 3, 1, 3, 0, 4, 1, 2, 1, 2, 0, 3, 1, 2, 1, 1, 2, 2, 0, 1, 2, 2, 0, 1, 0, 3, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 3, 3, 2, 1, 2, 0, 2, 0, 4, 0, 2, 2, 3, 1, 3, 2, 3, 1, 3, 1

Offset: 1

Author

Antti Karttunen, Jan 15 2021

Keywords

• nonn

Comments

Binary weight of A291759(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000120, A048673, A081603, A286585, A291759, A292252.

Cf. A340377 (positions of zeros).

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291759(n) = A289814(A048673(n));
A340379(n) = hammingweight(A291759(n));

Formula

a(n) = A081603(A048673(n)) = A000120(A291759(n)).

a(n) = (A286585(n) - A340378(n)) / 2.

For all n >= 1, a(n) >= A292252(n).