%I #20 Jul 04 2018 20:25:14

%S 1,2,4,8,16,15,9,10,5,14,24,19,18,22,20,61,52,34,12,32,26,11,13,47,35,

%T 3,29,28,17,51,44,41,36,33,31,40,38,30,205,191,147,134,71,68,37,77,39,

%U 69,49,54,53,62,63,64,60,67,66,100,93,92,86,78,75,82,89,96,57,126,122,27,23,76,70,72,135,129,125,65,59,825

%N Lexicographically first sequence of distinct integers whose concatenation of digits is the same as the concatenation of the digits of the absolute differences between consecutive terms.

%C This sequence might not be a permutation of A000027 (the positive numbers). After 18000 terms the smallest integer not yet present is 42. This 42 will perhaps never show.

%C From _Rémy Sigrist_, Jul 04 2018: (Start)

%C In fact, a(18420) = 42; however that this sequence is a permutation of the natural numbers remains an open question.

%C If we drop the unicity constraint, then we obtain A210025.

%C If moreover we impose that the sequence be nondecreasing, then we obtain A100787.

%C (End)

%H Jean-Marc Falcoz, <a href="/A301807/b301807.txt">Table of n, a(n) for n = 1..15032</a>

%e (The first members of the equalities hereunder must be seen as absolute differences between the successive pairs of adjacent terms:)

%e 1 - 2 = 1

%e 2 - 4 = 2

%e 4 - 8 = 4

%e 8 - 16 = 8

%e 16 - 15 = 1

%e 15 - 9 = 6

%e 9 - 10 = 1

%e 10 - 5 = 5

%e 5 - 14 = 9

%e 14 - 24 = 10

%e 24 - 19 = 5

%e 19 - 18 = 1, etc.

%e We see that the first and the last column present the same digit succession: 1, 2, 4, 8, 1, 6, 1, 5, 9, 1, 0, 5, 1, ...

%Y Cf. A301743 for the same idea with additions of adjacent terms instead of absolute differences.

%Y Cf. A100787, A210025.

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 27 2018