A101319 a(1) = 1; a(n) = (largest odd divisor of a(n-1))th smallest positive integer not yet in the sequence.

1, 2, 3, 6, 7, 12, 8, 4, 5, 14, 17, 28, 18, 21, 35, 50, 40, 15, 30, 31, 51, 72, 23, 43, 66, 56, 20, 16, 9, 27, 54, 55, 87, 120, 38, 45, 79, 115, 153, 192, 13, 37, 73, 112, 26, 41, 81, 126, 105, 152, 52, 42, 59, 104, 44, 36, 33, 78, 88, 46, 67, 124, 80, 24, 19, 64, 10, 32, 11, 58

Offset: 1

Author

Leroy Quet, Dec 23 2004

Keywords

• nonn

Comments

It seems likely, but not certain, that this sequence is a permutation of the positive integers, which it is if and only if there are an infinite number of powers of 2 in the sequence.

Examples

			a(6) = 12 and the highest odd divisor of 12 is 3. Among the first 6 terms of the sequence is not 4, 5, 8, 9, ... and the 3rd of these is 8, which is therefore a(7).
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Nest[Append[#, Complement[Range[Max[#] + (r = #[[-1]]/2^IntegerExponent[#[[-1]], 2])], #][[r]]] &, {1}, 69] (* Ivan Neretin, Sep 03 2018 *)

Extensions

More terms from Hans Havermann, Dec 24 2004