A169956 Lexicographically earliest sequence with positive integers satisfying a(a(n)) = 2*n+2.

2, 4, 5, 6, 8, 10, 9, 12, 16, 14, 13, 18, 24, 22, 17, 20, 32, 26, 21, 34, 40, 30, 25, 28, 48, 38, 29, 50, 56, 46, 33, 36, 64, 42, 37, 66, 72, 54, 41, 44, 80, 70, 45, 82, 88, 62, 49, 52, 96, 58, 53, 98, 104, 78, 57, 60, 112, 102, 61, 114, 120, 94, 65, 68, 128, 74

Offset: 1

Author

Eric Angelini, Aug 02 2010

Keywords

• nonn
• easy
• look

Comments

Previous name was: Similar to A080653, but without the "monotonically increasing sequence" condition.

Sequence contains all the even numbers and odd numbers k such that k mod 4 = 1. - Yifan Xie, Jul 05 2022

Examples

			For n=3, a(3) must satisfy a(a(3)) = 2*3+2 = 8. If a(3) = 0, we get 8 = a(a(3)) = a(0) = 1, so a(3) > 0. Using the same method twice we get a(3) > 2. If a(3) = 3, hence 3 = a(3) = a(a(3)) = 8, so a(3) > 3. If a(3) = 4, using a(2) = 4 we get 8 = a(a(3)) = a(4) = 2*2+2 = 6, so a(3) > 4. If a(3) = 5, there are no conflicts using the definition, so a(3) = 5. - _Yifan Xie_, Jul 05 2022
		

Links

• Yifan Xie, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A080653, A079905, A169957.

Formula

From Yifan Xie, Jul 05 2022: (Start)

a(A169957(n)-1) = 2*n for n > 1.

a(4*n-1) = 4*n+1 for n >= 1.

a(4*n+1) = 8*n for n >= 1. (End)

Extensions

New name and more terms from Yifan Xie, Jul 05 2022

a(23) corrected by Yifan Xie, Jul 05 2022