A365722 The number of prime factors (with multiplicity) in A356867(1+n), where A356867 is Sycamore's Doudna variant D(3).

0, 1, 1, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 4, 5, 3, 1, 2, 2, 2, 3, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 4, 5, 4, 3, 4, 4, 4, 5, 5, 5, 6, 4, 2, 3, 3, 3, 4, 4, 4, 5, 4, 3, 4, 4, 4, 5, 5, 5, 6, 5, 4, 5, 5, 5, 6, 6, 6, 7, 4, 1, 2, 2, 2, 3, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 4, 5, 4, 3, 4, 4, 4, 5, 5, 5

Offset: 0

Author

Antti Karttunen, Sep 17 2023

Keywords

• nonn
• base

Comments

Sum of digits minus the number of trailing 2's in the base-3 representation of n (A007089).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..59049

Crossrefs

Cf. A001222, A007089, A007949, A053735, A356867, A365719, A365721.

Cf. also A000120.

Programs

PARI

A365722(n) = (sumdigits(n,3)-valuation(1+n,3));

PARI

A365722(n) = bigomega(A356867(1+n)); \\ Uses also the program given in A356867.

Formula

a(n) = A001222(A356867(1+n)) = A001222(A365719(n)).

a(n) = A053735(n) - A007949(1+n).

a(n) >= A365721(n).