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 A318225 Lexicographically earliest sequence of positive terms such that the concatenation of two consecutive terms is always unique. 2

%I

%S 1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,10,1,11,2,2,3,2,4,2,5,2,6,2,7,2,

%T 8,2,9,2,10,2,11,3,3,4,3,5,3,6,3,7,3,8,3,9,3,10,3,11,4,4,5,4,6,4,7,4,

%U 8,4,9,4,10,4,11,5,5,6,5,7,5,8,5,9,5,10,5

%N Lexicographically earliest sequence of positive terms such that the concatenation of two consecutive terms is always unique.

%C In other words, for any distinct i and j, A066686(a(i), a(i+1)) <> A066686(a(j), a(j+1)).

%C The sequence b such that for any n > 0, b(n) = A066686(a(n), a(n+1)), satisfies b(n) = A303446(n+1) for n = 1..116 and b(117) <> A303446(118).

%C The sequence contains long runs of consecutive terms where one term out of two equals 1.

%H Rémy Sigrist, <a href="/A318225/b318225.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A318225/a318225.png">Logarithmic density plot of the first 300000000 terms</a>

%H Rémy Sigrist, <a href="/A318225/a318225.txt">C++ program for A318225</a>

%e The first terms, alongside the concatenation of a(n) and of a(n+1), are:

%e n a(n) A066686(a(n), a(n+1))

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

%e 1 1 11

%e 2 1 12

%e 3 2 21

%e 4 1 13

%e 5 3 31

%e 6 1 14

%e 7 4 41

%e 8 1 15

%e 9 5 51

%e 10 1 16

%e 11 6 61

%e 12 1 17

%e 13 7 71

%e 14 1 18

%e 15 8 81

%e 16 1 19

%e 17 9 91

%e 18 1 110

%e 19 10 101

%e 20 1 111

%e 21 11 112

%e 22 2 22

%e 23 2 23

%e 24 3 32

%e 25 2 24

%o (C++) See Links section.

%Y Cf. A066686, A303446.

%K nonn,base,look

%O 1,3

%A _Rémy Sigrist_, Aug 21 2018

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Last modified September 18 01:28 EDT 2021. Contains 347504 sequences. (Running on oeis4.)