A176869 Numbers that are the maximum value attained by the Collatz (3x+1) iteration of some odd number.

1, 16, 40, 52, 64, 88, 100, 112, 136, 148, 160, 184, 196, 208, 232, 244, 256, 280, 304, 340, 352, 400, 424, 448, 472, 520, 532, 544, 592, 616, 628, 640, 688, 712, 724, 736, 784, 808, 820, 832, 868, 904, 916, 928, 952, 964, 976, 1024, 1048, 1072, 1108, 1120

Offset: 1

Author

T. D. Noe, Apr 27 2010

Keywords

• nonn

Comments

Here the 3x+1 steps and the halving steps are applied separately. We use odd numbers because then the Collatz iteration always increases to a maximum value before (hopefully) going to 1. This is a subsequence of A033496. Except for the first term, all these numbers appear to equal 4 (mod 12). Some terms are the maximum value for the Collatz iteration of many numbers. For example, 9232 is the maximum value of the Collatz iteration of 408 odd numbers, the smallest of which is 27.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A025586 (maximum value in the Collatz iteration of n)