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

1,5

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

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.

Prog

(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));

Crossrefs

Even bisection of A341353.

Cf. A000040, A007949, A156552, A341355.

Cf. A329604 (positions of nonzero terms).

Sequence in context: A057918 A242192 A016380 * A203945 A212663 A341774

Adjacent sequences: A341351 A341352 A341353 * A341355 A341356 A341357

Keyword

nonn

Author

Antti Karttunen, Feb 14 2021

Status

approved