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A129599 Prime-factorization encoded partition code for the Łukasiewicz-word, variant of A129593.

%I A129599 #9 Oct 16 2015 23:01:05
%S A129599 1,3,25,25,343,35,35,343,35,14641,847,847,847,55,847,55,847,14641,847,
%T A129599 55,847,847,55,371293,24167,24167,1573,1183,24167,1183,1573,24167,
%U A129599 1183,1183,1183,1183,65,24167,1183,1183,1183,65,1573,1183,24167
%N A129599 Prime-factorization encoded partition code for the Łukasiewicz-word, variant of A129593.
%C A129599 In addition to all the automorphisms whose signature permutation satisfies the more restricted condition A127301(SP(n)) = A127301(n) for all n, there are also general tree-rotating automorphisms like *A057501, *A057502, *A069771 and *A069772 that satisfy also the condition A129599(SP(n)) = A129599(n) for all n. However, in contrast to A129593 this is not invariant under the automorphism *A072797. A000041(n) distinct values (seem to) occur in each range [A014137(n)..A014138(n)].
%H A129599 A. Karttunen, <a href="/A129599/b129599.txt">Table of n, a(n) for n = 0..625</a>
%H A129599 OEIS Wiki, <a href="/wiki/Łukasiewicz_words">Łukasiewicz words</a>
%H A129599 <a href="/index/Lu#Lukasiewicz">Index entries for sequences related to Łukasiewicz</a>
%F A129599 Construction: add one to each number of the Łukasiewicz-word of a general plane tree encoded by A014486(n) (i.e. A079436(n)) except the first number, sort the numbers into ascending order and interpreting it as a partition of a natural number, encode it in the manner explained in A129595.
%e A129599 The terms A079436(5), A079436(6) and A079436(8) are 2010, 2100 and 1110. After adding one to each number except the first one we get 2121, 2211 and 1221, each one which produces partition 1+1+2+2. Converting it to prime-exponents like explained in A129595, we get 2^0 * 3^0 * 5^1 * 7^1 = 35, thus a(5) = a(6) = a(8) = 35.
%Y A129599 Variant: A129593.
%K A129599 nonn
%O A129599 0,2
%A A129599 _Antti Karttunen_, May 01 2007