A306546 - OEIS

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

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OFFSET

1,1

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

FORMULA

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

PROG

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

CROSSREFS

Cf. A006370, A016777, A000265.

Sequence in context: A064947 A369894 A059926 * A138775 A209385 A121529

Adjacent sequences: A306543 A306544 A306545 * A306547 A306548 A306549

KEYWORD

nonn,easy

AUTHOR

Aidan Simmons, Feb 22 2019

STATUS

approved