A340379 - OEIS

%I #9 Jan 16 2021 06:39:19

%S 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,

%T 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,

%U 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

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

%C Binary weight of A291759(n).

%H Antti Karttunen, <a href="/A340379/b340379.txt">Table of n, a(n) for n = 1..65537</a>

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

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

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

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

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

%o A048673(n) = (A003961(n)+1)/2;

%o A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814

%o A291759(n) = A289814(A048673(n));

%o A340379(n) = hammingweight(A291759(n));

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

%Y Cf. A340377 (positions of zeros).

%K nonn

%O 1,6

%A _Antti Karttunen_, Jan 15 2021