A226629 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k=A226630(n).

3, 1, 2, 1, 8, 1, 1, 1, 1, 3, 1, 1, 2, 1, 3, 1, 2, 5, 35, 2, 1, 2, 1, 6, 9, 136, 1, 1, 4, 2, 1, 1, 16, 3, 8, 8, 1, 9, 1, 2, 1, 16, 7, 9, 1, 1, 1, 26, 21, 13, 3, 4, 3, 2, 2, 38, 4, 2, 29, 3, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 8, 8, 1, 34, 33, 3, 1, 3, 1, 1, 1, 96, 4

Offset: 1

Author

Geoffrey H. Morley, Jun 13 2013

Keywords

• nonn

Comments

A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.

The 3x-k function T_k is defined by T_k(x) = x/2 if x is even, (3x-k)/2 if x is odd, where k is odd.

For primitive cycles, GCD(k,6)=1.

Links

• Geoffrey H. Morley, Table of n, a(n) for n = 1..600

Crossrefs

a(n) is the number of terms in the n-th row of A226623 to A226627.

Cf. A226613, A226679.

Formula

a(n) = A226628(n+1) - A226628(n).