A267110 If A051135(n) = 1, then a(n) = A004001(n) - 1, otherwise a(n) = n - A004001(n).

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 5, 7, 6, 7, 8, 8, 9, 10, 11, 9, 12, 13, 10, 14, 11, 12, 15, 13, 14, 15, 16, 16, 17, 18, 19, 20, 17, 21, 22, 23, 18, 24, 25, 19, 26, 20, 21, 27, 28, 22, 29, 23, 24, 30, 25, 26, 27, 31, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 33, 38, 39, 40, 41, 34, 42, 43, 44, 35, 45, 46, 36, 47

Offset: 1

Author

Antti Karttunen, Jan 16 2016

Keywords

• nonn
• look

Comments

For n > 1, a(n) gives the contents of the parent of the node which contains n in A267112-tree.

Each n > 0 occurs exactly twice, in positions A088359(n) and A087686(n+1).

The sequence maps each n > 1 to a number which is one digit shorter in binary system (cf. "Other identities"). This follows because A004001 is monotonic and A004001(2^n) = 2^(n-1) (see properties (2) and (3) given on page 227 of Kubo & Vakil paper, or page 3 in PDF), and also how the frequency counts Q_n for A004001 are recursively constructed (see Kubo & Vakil paper, p. 229 or A265332 for the illustration).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A004001, A051135, A070939, A087686, A088359, A265332, A267108, A267109, A267112.

Programs

Scheme

(define (A267110 n) (if (= 1 (A051135 n)) (- (A004001 n) 1) (- n (A004001 n))))

Formula

If A051135(n) = 1 [Equally: if A265332(n) = 1], then a(n) = A004001(n) - 1, otherwise a(n) = n - A004001(n).

Other identities. For all n >= 2:

A070939(a(n)) = A070939(n) - 1. [See Comments section.]