A153832 Atavistic Index Sequence to A089840 computed for ENIPS.

0, 15, 3617, 3677, 3690, 3721, 3744

Offset

0,2

Comments

Recursive transformation ENIPS for Catalan bijections has a well-defined inverse (see the definition & comments at A122204). For all Catalan bijections in A089840 that inverse produces a bijection which is itself in A089840. This sequence gives the indices to those positions where each ("primitive", non-recursive bijection) of A089840(n) occurs "atavistically" amongst the more complex recursive bijections in A122204. I.e. A122204(a(n)) = A089840(n). Similarly, other "atavistic forms" resurface as: A122287(a(n)) = A122201(n), A122286(a(n)) = A122203(n) and A122202(a(n)) = A122284(n). See also comments at A153833.

There exists similar atavistic index sequences computed for FORK (A122201) and KROF (A122202). Both start as 0,1654720,... (see A129604). This implies that regardless of how complex recursive derivations from A089840 one forms by repeatedly applying SPINE, ENIPS, FORK and/or KROF in some order (finite number of times), all the original primitive non-recursive elements of A089840 will eventually appear at some positions.

Other known terms: a(12)=65167, a(13)=65178, a(14)=65236, a(15)=169, a(16)=65302, a(22)-a(44) = 1656351, 1656576, 1656777, 1656628, 1656704, 1659507, 1659538, 1659653, 1659798, 1659685, 1659830, 1660155, 1660582, 1660439, 1660476, 1660621, 1660196, 1661073, 1660930, 1660859, 1661004, 1661287, 1661360.

Links

Table of n, a(n) for n=0..6.

A. Karttunen, C-program for computing the initial terms of this sequence

Formula

a(n) = A089839bi(n,A153834(A089843(n))).

Crossrefs

Cf. A153833, A089839.

Sequence in context: A182283 A194479 A262019 * A198524 A208463 A374796

Adjacent sequences: A153829 A153830 A153831 * A153833 A153834 A153835

Keyword

nonn

Author

Antti Karttunen, Jan 07 2009

Status

approved