This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A083928 #9 Jan 30 2024 08:23:35 %S A083928 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %T A083928 0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %U A083928 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 %N A083928 Inverse function of N -> N injection A080298. %C A083928 a(1)=0 because A080298(0)=1, but a(n) = 0 also for those n which do not occur as values of A080298. All positive natural numbers occur here once. %C A083928 For example, A057163 = A083928(A057163(A080298(n))), i.e. Catalan bijection A057163 embeds into itself in scale n:2n+1 using the obvious zigzag-tree -> binary tree embedding. %H A083928 Antti Karttunen, <a href="https://web.archive.org/web/20021212104851/http://ndirty.cute.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> %o A083928 (Scheme-function showing the essential idea. For the full source, follow the "Catalan bijections" link.) %o A083928 (define (ZigzagTree2BinTree_if_possible gt) (call-with-current-continuation (lambda (e) (let recurse ((gt gt)) (cond ((equal? gt '(() . ())) (list)) ((not (pair? gt)) (e '())) (else (cons (recurse (car gt)) (recurse (cdr gt))))))))) %Y A083928 a(A080298(n)) = n for all n. Cf. A083925-A083927, A083929, A083935. %K A083928 nonn %O A083928 0,40 %A A083928 _Antti Karttunen_, May 13 2003