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A226660
Smallest positive integer k with a primitive cycle of n positive integers (n>1) under iteration by the Collatz-like 3x+k function.
3
1, 5, 7, 5, 11, 17, 13, 97, 59, 19, 55, 233, 11, 73, 25, 29, 47, 215, 41, 103, 145, 31, 13, 119, 131, 5, 47, 53, 67, 17, 337, 125, 115, 485, 133, 127, 49, 119, 191, 293, 133, 23, 79, 103, 191, 167, 91, 409, 329, 217, 109, 449, 241, 361, 353, 1303, 239, 149, 73
OFFSET
2,2
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.
For n>1, T_k has a primitive cycle of length n which includes 1 when k = A036563(n) = 2^n-3. So a(n) <= 2^n-3.
LINKS
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey H. Morley, Jul 05 2013
STATUS
approved