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

1,1

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

Links

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

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)

Example

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

Crossrefs

Cf. A080653, A079905, A169957.

Sequence in context: A229133 A015844 A114318 * A342495 A035500 A080653

Adjacent sequences: A169953 A169954 A169955 * A169957 A169958 A169959

Keyword

nonn,easy,look

Author

Eric Angelini, Aug 02 2010

Extensions

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

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

Status

approved