cp's OEIS Frontend

A191654 First repeating AN iterates. The AN (Adjective-before-Noun) 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.

%I A191654 #9 Feb 13 2014 13:24:45
%S A191654 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,
%T A191654 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,
%U A191654 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
%N A191654 First repeating AN iterates.  The AN (Adjective-before-Noun) 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.
%C A191654 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.
%C A191654 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.
%t A191654 (* Program computes the AN segment starting with 0. *)
%t A191654 adjectiveNoun[s_] := Flatten@Transpose@({(Count[s, #1] &) /@ #1, #1} &)[Range[0, Max[s]]];
%t A191654 NestList[adjectiveNoun[#1] &, adjectiveNoun[{0}], 7]
%t A191654 (* Next program, the AN segment starting with 1. *)
%t A191654 adjectiveNoun[s_] := Flatten@Transpose@({(Count[s, #1] &) /@ #1, #1} &)[Range[0, Max[s]]];
%t A191654 NestList[adjectiveNoun[#1] &, adjectiveNoun[{1}], 7]
%t A191654 (* ...and so on.  By _Peter J. C. Moses_, Jun 03 2011 *)
%Y A191654 Cf. A109973.
%K A191654 nonn
%O A191654 1,3
%A A191654 _Clark Kimberling_, Jun 10 2011