A226665 Conjectured record-breaking maximal values, for ascending positive integers k, of the minimal elements of the primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

1, 347, 7055, 177337, 212665, 219913, 379541, 413803, 822535, 1391321, 8013899, 21619279, 21834347, 28306063, 37550317, 168536521, 189763177

Offset

1,2

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

Table of n, a(n) for n=1..17.

Example

a(1)=1 because {1,2}, with minimal element 1, is the only known '3x+1' cycle of positive integers.
k=5 is the next value of k>1 with GCD(k,6)=1. The minimal element in each of the five known primitive '3x+5' cycles of positive integers is 1, 19, 23, 187 and 347. 347>a(1) so a(2)=347.

Crossrefs

k = A226666(n).

Cf. A226607, A226681.

Sequence in context: A012868 A343303 A226669 * A185713 A264384 A323999

Adjacent sequences: A226662 A226663 A226664 * A226666 A226667 A226668

Keyword

nonn

Author

Geoffrey H. Morley, Jun 16 2013

Status

approved