A153833 Atavistic Index Sequence to A089840 computed for SPINE.

0, 21, 3613, 3771, 3906, 3929, 3783

Offset: 0

Author

Antti Karttunen, Jan 07 2009

Keywords

• nonn

Comments

Recursive transformation SPINE for Catalan bijections has a well-defined inverse (see the definition & comments at A122203). 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 A122203. I.e. A122203(a(n)) = A089840(n). Similarly, other "atavistic forms" resurface as: A122288(a(n)) = A122202(n), A122285(a(n)) = A122204(n) and A122201(a(n)) = A122283(n). See also comments at A153832.

Other known terms: a(17)-a(44): 65352, 65359, 65604, 65739, 251, 1656303, 1656426, 1656552, 1656628, 1656479, 1661655, 1661816, 1666720, 1684006, 1684221, 1667042, 1667007, 1684152, 1661799, 1661676, 1666759, 1684081, 1684437, 1667151, 1684509, 1667187, 1661961, 1661944.

Links

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

Crossrefs

Cf. A153832, A089839.

Formula

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