A082857 Inverse function of N -> N injection A082856.

0, 1, 0, 2, 0, 3, 0, 6, 0, 0, 0, 4, 0, 0, 0, 14, 0, 0, 0, 0, 0, 7, 0, 16, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 5, 0, 0, 0, 15, 0, 0, 0, 11, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 123, 0, 0, 0, 0, 0, 8, 0, 19, 0, 0, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 20, 0, 53, 0, 0, 0, 0, 0, 0, 0, 154, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 155

Offset

0,4

Comments

a(n) = 0 for those n which do not occur as the values of A082856. All positive natural numbers occur here once.

Links

Table of n, a(n) for n=0..119.

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)

Formula

a(A082856(n)) = n for all n.

Prog

(Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)
(define A082857 (compose-funs A080300 parenthesization->binexp decode-A082856-code))
(define (decode-A082856-code code) (call-with-current-continuation (lambda (exit) (let recurse ((code code)) (cond ((zero? code) (list)) ((even? code) (exit '())) (else (let ((even-bits (A059905 (floor->exact (/ code 2)))) (odd-bits (A059906 (floor->exact (/ code 2))))) (cons (recurse odd-bits) (recurse even-bits)))))))))

Crossrefs

Cf. A082856, A072634-A072637, A075173-A075174.

Sequence in context: A117175 A228086 A090482 * A208092 A081155 A348075

Adjacent sequences: A082854 A082855 A082856 * A082858 A082859 A082860

Keyword

nonn

Author

Antti Karttunen, May 06 2003

Status

approved