A306546 Modified Collatz Map such that odd numbers are treated the same, but even numbers have all factors of 2 removed.

4, 1, 10, 1, 16, 3, 22, 1, 28, 5, 34, 3, 40, 7, 46, 1, 52, 9, 58, 5, 64, 11, 70, 3, 76, 13, 82, 7, 88, 15, 94, 1, 100, 17, 106, 9, 112, 19, 118, 5, 124, 21, 130, 11, 136, 23, 142, 3, 148, 25, 154, 13, 160, 27, 166, 7, 172, 29, 178, 15, 184, 31, 190, 1, 196, 33, 202, 17, 208, 35, 214, 9, 220, 37, 226, 19, 232

Offset: 1

Author

Aidan Simmons, Feb 22 2019

Keywords

• nonn
• easy

Comments

All numbers that reach 1 under normal Collatz iteration will reach 1 through this mapping. This sequence combines all consecutive even number halvings into one step. This will decrease steps to completion compared to normal Collatz iteration for all starting points other than 1 and 2, drastically in most cases. If this mapping is applied upon A000265, the sequence generated when the even operation is applied initially, then further iteration through this modified mapping will have all entries synchronize to all either be odd or all be even for any given step.

Links

• Aidan Simmons, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A016777, A000265.

Programs

PARI

a(n) = if (n%2, 3*n+1, n >> valuation(n, 2)); \\ Michel Marcus, Mar 05 2019

Formula

For any even n, a(n) = A000265(n). For any odd n, a(n) = 3n+1.