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Search: id:A129599
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| A129599 |
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Prime-factorization encoded partition code for the Lukasiewicz-word, variant of A129593. |
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+0
2
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| 1, 3, 25, 25, 343, 35, 35, 343, 35, 14641, 847, 847, 847, 55, 847, 55, 847, 14641, 847, 55, 847, 847, 55, 371293, 24167, 24167, 1573, 1183, 24167, 1183, 1573, 24167, 1183, 1183, 1183, 1183, 65, 24167, 1183, 1183, 1183, 65, 1573, 1183, 24167
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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)].
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..625
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FORMULA
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Construction: add one to each number of the Lukasiewicz-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.
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EXAMPLE
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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.
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CROSSREFS
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Variant: A129593.
Sequence in context: A085836 A073916 A076962 this_sequence A042899 A051280 A145609
Adjacent sequences: A129596 A129597 A129598 this_sequence A129600 A129601 A129602
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), May 01 2007
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