

A191654


First repeating AN iterates. The AN (AdjectivebeforeNoun) function of a finite sequence s of nonnegative integers is the finite sequence a,0,b,1,c,2,...m,z, where a=#0's in s, b=#1's in s,..., m=#z's in s, where m is the greatest term in s.


2



1, 0, 2, 1, 3, 2, 2, 3, 1, 0, 3, 1, 1, 2, 3, 3, 1, 0, 3, 1, 1, 2, 3, 3, 1, 0, 3, 1, 2, 2, 3, 3, 1, 4, 1, 0, 4, 1, 2, 2, 2, 3, 2, 4, 1, 5, 1, 0, 5, 1, 2, 2, 2, 3, 1, 4, 2, 5, 1, 6, 1, 0, 5, 1, 4, 2, 1, 3, 1, 4, 1, 5, 2, 6, 1, 7, 1, 0, 6, 1, 4, 2, 1, 3, 1, 4, 1, 5, 1, 6, 2, 7, 1, 8
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OFFSET

1,3


COMMENTS

This is a concatenation of finite segments. The first segment is 10213223, obtained by writing AN iterates starting with 0 until repetition occurs: 0, 10, 1011, 1031, 10210213, 20312213, 10213223, 10213223. It may help to speak your way along: write 0 and say one 0  that's 10; then say one 0 and one 1  that's 1011; and so on, until reaching the repeating segment 10213223. This segment is a fixed point of the AN function.
The second segment arises in the same way starting with 1, and likewise for further segments. The resulting segments concatenate to form A191654 in the same manner that NA segments form A109973. Indeed, A191654 can be easily read from A109973 by reversing pairs of terms. Thus, the open questions at A109973 apply also to A191654.


LINKS

Table of n, a(n) for n=1..94.


MATHEMATICA

(* Program computes the AN segment starting with 0. *)
adjectiveNoun[s_] := Flatten@Transpose@({(Count[s, #1] &) /@ #1, #1} &)[Range[0, Max[s]]];
NestList[adjectiveNoun[#1] &, adjectiveNoun[{0}], 7]
(* Next program, the AN segment starting with 1. *)
adjectiveNoun[s_] := Flatten@Transpose@({(Count[s, #1] &) /@ #1, #1} &)[Range[0, Max[s]]];
NestList[adjectiveNoun[#1] &, adjectiveNoun[{1}], 7]
(* ...and so on. By Peter J. C. Moses, Jun 03 2011 *)


CROSSREFS

Cf. A109973.
Sequence in context: A177062 A133924 A023135 * A205784 A066272 A237130
Adjacent sequences: A191651 A191652 A191653 * A191655 A191656 A191657


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jun 10 2011


STATUS

approved



