A338196 The integers sorted according to the maximum number in their Collatz (3*x+1) orbit, and in the case of a tie, sorted according to their value.

1, 2, 4, 8, 3, 5, 6, 10, 12, 16, 20, 24, 32, 13, 26, 40, 48, 7, 9, 11, 14, 17, 18, 22, 28, 34, 36, 44, 52, 56, 21, 42, 64, 68, 72, 80, 84, 19, 25, 29, 38, 50, 58, 76, 88, 96, 33, 66, 100, 104, 37, 74, 112, 116, 128, 132, 45, 90, 136, 144, 49, 98, 148, 152, 15

Offset: 1

Author

Hugo Pfoertner, Oct 21 2020

Keywords

• nonn

Comments

Assuming the validity of the Collatz conjecture, this sequence is a permutation of the natural numbers.

Examples

			a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 8 are already the maximum in their orbit.
a(5) = 3, a(6) = 5, a(7) = 6, a(8) = 10, a(9) = 12, and a(10) = 16 all have an orbit with 16 as maximum and are therefore sorted by their size.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A338196

Crossrefs

Cf. A006370, A006577, A025586, A087255.

Programs

PARI

See Links section.