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 A083927 Inverse function of N -> N injection A057123. 17
 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS a(0)=0 because A057123(0)=0, but a(n) = 0 also for those n which do not occur as values of A057123. All positive natural numbers occur here once. If g(n) = A083927(f(A057123(n))) then we can say that Catalan bijection g embeds into Catalan bijection f in scale n:2n, using the obvious binary tree -> general tree embedding. E.g. we have: A057163 = A083927(A057164(A057123(n))), A057117 = A083927(A072088(A057123(n))), A057118 = A083927(A072089(A057123(n))), A069770 = A083927(A072796(A057123(n))), A072797 = A083927(A072797(A057123(n))). LINKS A. Karttunen, Gatomorphisms PROG (Scheme-function showing the essential idea. For the full source, follow the "Catalan bijections" link.) (define (Tree2BinTree_if_possible gt) (call-with-current-continuation (lambda (e) (let recurse ((gt gt)) (cond ((not (pair? gt)) gt) ((eq? 2 (length gt)) (cons (recurse (car gt)) (recurse (cadr gt)))) (else (e '()))))))) CROSSREFS a(A057123(n)) = n for all n. Cf. A083925-A083926, A083928-A083929, A083935. Sequence in context: A173956 A306078 A284273 * A154724 A232747 A130460 Adjacent sequences:  A083924 A083925 A083926 * A083928 A083929 A083930 KEYWORD nonn AUTHOR Antti Karttunen May 13 2003 STATUS approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)