cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A226682 Integer k associated with the conjectured record-breaking maximal value A226681(n) of the minimal elements of primitive Collatz-like 3x-k cycles.

Original entry on oeis.org

1, 11, 17, 19, 23, 131, 311, 467, 3377, 5137, 66781, 76085, 143369
Offset: 1

Views

Author

Geoffrey H. Morley, Jun 16 2013

Keywords

Crossrefs

Cf. A226666.

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.

Original entry on oeis.org

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

Views

Author

Geoffrey H. Morley, Jun 16 2013

Keywords

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

			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).
Showing 1-2 of 2 results.