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A300958 Fixed points of A300956.

%I A300958 #13 Mar 20 2018 20:35:49
%S A300958 0,15,21,21141,21156,21162,40095,40110,40116,72171,72186,72192,93312,
%T A300958 93327,93333,112266,112281,112287,124659,124674,124680,145800,145815,
%U A300958 145821,164754,164769,164775,181521,181536,181542,202662,202677,202683,221616,221631
%N A300958 Fixed points of A300956.
%C A300958 In ternary representation:
%C A300958 - each term has as many 1's as 2's and the set of positions of 1's is the image under A300956 of the set of positions of 2's and vice versa (where the position 0 corresponds to the unit ternary digit),
%C A300958 - the digit at position a(k) of a term is always zero for any k > 0; in particular, as a(1) = 0, all terms are divisible by 3.
%C A300958 To compute a(n):
%C A300958 - consider the sequence of integers k, say f, such that A300956(k) < k,
%C A300958 - the sequence f starts: 2, 9, 10, 11, 17, 18, 19, 20, 23, 24, 25, 26, 19683, ...
%C A300958 - let g(k, t) be defined for k > 0 and t = 0..2 as: g(k, 0) = 0, g(k, 1) = 3^f(k) + 2 * 3^A300956(f(k)), g(k, 2) = 2 * 3^f(k) + 3^A300956(f(k)),
%C A300958 - let Sum_{i = 0..m} t_i * 3^i be the ternary representation of n-1,
%C A300958 - then a(n) = Sum_{i = 0..m} g(i+1, t_i).
%H A300958 Rémy Sigrist, <a href="/A300958/b300958.txt">Table of n, a(n) for n = 1..6561</a>
%H A300958 Rémy Sigrist, <a href="/A300958/a300958.gp.txt">PARI program for A300958</a>
%F A300958 A062756(a(n)) = A081603(a(n)).
%o A300958 (PARI) See Links section.
%Y A300958 Cf. A062756, A081603, A300956.
%K A300958 nonn,base
%O A300958 1,2
%A A300958 _Rémy Sigrist_, Mar 17 2018