A123481 Record n for the sequence A006666(n)/log(n), for n > 1; i.e., the n at which the number of steps to 1 for the halving-Collatz iteration divided by log(n) sets a new maximum.

2, 3, 7, 9, 27, 230631, 626331, 837799, 1723519, 3732423, 6649279, 8400511, 63728127, 3743559068799, 100759293214567, 104899295810901231

Offset

1,1

Comments

These numbers (for n > 2, at least) are called "Abby-Normal" numbers by Dominici in the referenced paper (definition 21); 2 is included here to agree with the RECORDS transform convention. - D. S. McNeil, Mar 26 2009

Three further terms are known (see Roosendaal) but they may not be the next three terms. - N. J. A. Sloane, Oct 21 2012

Links

Table of n, a(n) for n=1..16.

D. Dominici, Working with 2s and 3s, arXiv:0704.1057

Eric Roosendaal, 3x+1 Completeness and Gamma Records - From N. J. A. Sloane, Oct 21 2012

Crossrefs

Sequence in context: A299437 A255393 A248037 * A107861 A109800 A152136

Adjacent sequences: A123478 A123479 A123480 * A123482 A123483 A123484

Keyword

nonn

Author

Diego Dominici (dominicd(AT)newpaltz.edu), Apr 16 2007

Extensions

Definition edited by D. S. McNeil, Mar 26 2009

Extended by D. S. McNeil, Mar 26 2009

a(13) from Donovan Johnson, Feb 16 2011

a(14)-a(16) from Roosendaal's table added by N. J. A. Sloane, Oct 21 2012

Status

approved