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A341354
Greatest k such that 3^k divides A156552(2*n); number of trailing 1-digits in the ternary expansion of A156552(n).
4
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).
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. A329604 (positions of nonzero terms).
Sequence in context: A057918 A242192 A016380 * A203945 A212663 A341774
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 14 2021
STATUS
approved