cp's OEIS Frontend

A301807 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.

%I A301807 #20 Jul 04 2018 20:25:14
%S A301807 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 A301807 3,29,28,17,51,44,41,36,33,31,40,38,30,205,191,147,134,71,68,37,77,39,
%U A301807 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 A301807 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 A301807 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 A301807 From _Rémy Sigrist_, Jul 04 2018: (Start)
%C A301807 In fact, a(18420) = 42; however that this sequence is a permutation of the natural numbers remains an open question.
%C A301807 If we drop the unicity constraint, then we obtain A210025.
%C A301807 If moreover we impose that the sequence be nondecreasing, then we obtain A100787.
%C A301807 (End)
%H A301807 Jean-Marc Falcoz, <a href="/A301807/b301807.txt">Table of n, a(n) for n = 1..15032</a>
%e A301807 (The first members of the equalities hereunder must be seen as absolute differences between the successive pairs of adjacent terms:)
%e A301807     1 -  2 =  1
%e A301807     2 -  4 =  2
%e A301807     4 -  8 =  4
%e A301807     8 - 16 =  8
%e A301807    16 - 15 =  1
%e A301807    15 -  9 =  6
%e A301807     9 - 10 =  1
%e A301807    10 -  5 =  5
%e A301807     5 - 14 =  9
%e A301807    14 - 24 = 10
%e A301807    24 - 19 =  5
%e A301807    19 - 18 =  1, etc.
%e A301807 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 A301807 Cf. A301743 for the same idea with additions of adjacent terms instead of absolute differences.
%Y A301807 Cf. A100787, A210025.
%K A301807 nonn,base
%O A301807 1,2
%A A301807 _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 27 2018