A341354 - OEIS

%I #15 Mar 11 2021 03:23:18

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A341354/b341354.txt">Table of n, a(n) for n = 1..65539</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

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

%o (PARI)

%o A007949(n) = valuation(n,3);

%o 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 };

%o A341354(n) = A007949(A156552(2*n));

%Y Even bisection of A341353.

%Y Cf. A000040, A007949, A156552, A341355.

%Y Cf. A329604 (positions of nonzero terms).

%K nonn

%O 1,5

%A _Antti Karttunen_, Feb 14 2021