OEIS A073057 Append Morphism

OEIS sequence A073057 by Roger L. Bagula is an initial 1,2,3,4 then repeatedly take the sequence so-far and append a copy of it expanded by morphism

1 -> 12, 2 -> 13, 3 -> 42, 4 -> 43

A073057 = 1,2,3,4, 1,2,1,3,4,2,4,3, 1,2,1,3,4,2,4,3,1,2,1,3,...

The PARI/GP code here is a mixture of code and description for calculating a term of A073057 from its index n. The appends give "morphism block" lengths which are Gould's sequence and finding which one contains n, and how far n is into it, gives a term.

The accompanying PDF shows state machines used, and alternate paperfolding curve "figure of 8" loops which result from taking the sequence values as segment directions E,N,S,W. is free software (free as in freedom), published under the terms of the GNU General Public License (v3 or higher). Download version 1, (24k, and sig)
a073057-diagrams.pdf (152 kbytes, 3 pages)
a073057-append-morphism-1.tar.gz (80k, and sig)

The sig files are Gnu PG ascii armoured signatures generated from my key. Just is the code and notes. The .tar.gz includes LaTeX+PGF source for the diagrams, and some slightly rough tools used for state machine manipulations and checking.

See my alternate paperfolding curve write-up for more on its segment directions, extents, etc.

This page Copyright 2021 Kevin Ryde.

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