A341354 Greatest k such that 3^k divides A156552(2*n); number of trailing 1-digits in the ternary expansion of A156552(n).

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

Offset: 1

Author

Antti Karttunen, Feb 14 2021

Keywords

• nonn

Comments

The 3-adic valuation of A156552(2*n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65539
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Even bisection of A341353.

Cf. A000040, A007949, A156552, A341355.

Cf. A329604 (positions of nonzero terms).

Programs

PARI

A007949(n) = valuation(n,3);
A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A341354(n) = A007949(A156552(2*n));

Formula

a(n) = A341353(2*n) = A007949(A156552(2*n)) = A007949(1+(2*A156552(n))).

For all n >= 1, a(A000040(2*n)) = a(n^2) = 0.