A226620 -id:A226620 - cp's OEIS frontend

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

Geoffrey H. Morley, Jul 02 2013

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.

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

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

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

A226621 Irregular array read by rows in which a(n) is the number of primitive '3x+k' cycles associated with A226619(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 1, 3, 1, 5, 5, 2, 1, 1, 3, 7, 1, 2, 5, 7, 3, 1, 1, 4, 8, 1, 1, 14, 14, 8, 4, 1, 1, 3, 12, 1, 6, 2, 1, 1, 14, 23, 20, 12, 2, 1, 1, 5, 15, 29, 1, 1, 1, 2, 5, 5, 42, 34, 25, 14, 5, 1, 1, 5, 16, 28, 2, 9, 1, 1, 1

Offset: 1

Geoffrey H. Morley, Jul 02 2013

The terms in row n are associated with cycles of length n (see A226619).

			The irregular array starts:
1, 1;
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 1, 3, 1, 1; ...

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

Cf. A226620.

cp's OEIS Frontend

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.

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