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Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the 3-adic valuation of a(n) equals the 2-adic valuation of a(n+1).
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%I #6 May 22 2018 20:32:41

%S 1,3,2,5,7,9,4,11,13,15,6,10,17,19,21,14,23,25,27,8,29,31,33,18,12,22,

%T 35,37,39,26,41,43,45,20,47,49,51,30,34,53,55,57,38,59,61,63,28,65,67,

%U 69,42,46,71,73,75,50,77,79,81,16,83,85,87,54,24,58,89

%N Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the 3-adic valuation of a(n) equals the 2-adic valuation of a(n+1).

%C See A298196 for a similar sequence and additional comments.

%C This sequence is a permutation of the natural number, with inverse A304882.

%C The only known fixed point is a(1) = 1.

%H Rémy Sigrist, <a href="/A304881/a304881.png">Colored scatterplot of the first 100000 terms</a> (where the color is function of A007814(a(n)))

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms, alongside their 2-adic and 3-adic valuations, are:

%e n a(n) v2 v3

%e -- ---- -- --

%e 1 1 0 0

%e 2 3 0 1

%e 3 2 1 0

%e 4 5 0 0

%e 5 7 0 0

%e 6 9 0 2

%e 7 4 2 0

%e 8 11 0 0

%e 9 13 0 0

%e 10 15 0 1

%e 11 6 1 1

%e 12 10 1 0

%e 13 17 0 0

%e 14 19 0 0

%e 15 21 0 1

%e 16 14 1 0

%e 17 23 0 0

%e 18 25 0 0

%e 19 27 0 3

%e 20 8 3 0

%Y Cf. A007814, A298196, A304882 (inverse).

%K nonn

%O 1,2

%A _Rémy Sigrist_, May 20 2018