A088721 Unique monotone sequence satisfying a(a(a(a(n)))) = 2n.

5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81

Offset: 4

Author

Colin Mallows, Oct 12 2003

Keywords

• easy
• nonn

Comments

For all k >= 0, there is a unique sequence satisfying a^(k+1)=2n. The first differences are 1^k, 2^1, 1^2k, 2^2, 1^4k, 2^4, 1^8k, ...

Links

• H.-K. Hwang, S. Janson, T.-H. Tsai. Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications. Preprint, 2016.
• H.-K. Hwang, S. Janson, T.-H. Tsai. Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications. ACM Transactions on Algorithms, 13:4 (2017), #47. DOI:10.1145/3127585.

Crossrefs

Cf. A007378, A003605, A088720.

Formula

First differences are 1^3, 2^1, 1^6, 2^2, 1^12, 2^4, 1^24, 2^8, ...