A226618 Irregular array read by rows in which row n lists the positive integers k in ascending order for which 1 is in a primitive cycle of n positive integers under iteration by the Collatz-like 3x+k function.

1, 5, 13, 29, 11, 61, 17, 125, 253, 509, 145, 203, 1021, 43, 2045, 55, 4093, 355, 1169, 8189, 137, 3275, 16381, 1129, 32765, 1007, 5957, 9361, 65533, 131069, 97, 52427, 262141, 643, 74897, 524285, 41, 1048573, 553, 28727, 110375, 2097149, 281, 673, 2075, 9731, 34663

Offset: 1

Author

Geoffrey H. Morley, Jul 02 2013

Keywords

• nonn
• tabf

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.

Examples

			The irregular array starts:
1;
5;
13;
29;
11, 61;
17, 125; ...
Row 1 is empty.
		

Links

• Geoffrey H. Morley, Rows 2..26 of array, flattened

Crossrefs

The first element in row n is A226616(n), and the last is A036563(n) = 2^n-3.

Cf. A226609, A226619.