A226619 Irregular array read by rows in which row n lists the integers k, in ascending order, for which there is a primitive cycle of n positive integers under iteration by the Collatz-like 3x+k function.

-1, 1, 1, -1, 5, -11, 7, 13, -49, 5, 23, 29, -179, -17, 11, 37, 55, 61, -601, -115, 17, 47, 101, 119, 125, -1931, -473, 13, 25, 35, 175, 229, 247, 253, -6049, -1675, -217, -31, 97, 269, 431, 485, 503, 509, -18659, -5537, -1163, -791, 59, 71, 145, 203, 295, 781, 943, 997, 1015, 1021

Offset

1,5

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.

We associate the cycle {0} with k = A226606(2) = 1.

For n>1 the first term of row n is 2^n-3^(n-1), and the last term is A036563(n) = 2^n-3.

Links

Geoffrey H. Morley, Rows 1..26 of array, flattened

Example

The irregular array starts:
-1, 1;
1;
-1, 5;
-11, 7, 13;
-49, 5, 23, 29; ...

Crossrefs

Cf. A226605, A226606, A226618, A226620, A226621.

Sequence in context: A172183 A088213 A226606 * A367705 A068419 A226586

Adjacent sequences: A226616 A226617 A226618 * A226620 A226621 A226622

Keyword

sign,tabf

Author

Geoffrey H. Morley, Jul 02 2013

Status

approved