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.

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

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Mar 27 2018

Keywords

• nonn
• base

Comments

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.

From Rémy Sigrist, Jul 04 2018: (Start)

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

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

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

(End)

Examples

			(The first members of the equalities hereunder must be seen as absolute differences between the successive pairs of adjacent terms:)
    1 -  2 =  1
    2 -  4 =  2
    4 -  8 =  4
    8 - 16 =  8
   16 - 15 =  1
   15 -  9 =  6
    9 - 10 =  1
   10 -  5 =  5
    5 - 14 =  9
   14 - 24 = 10
   24 - 19 =  5
   19 - 18 =  1, etc.
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, ...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..15032

Crossrefs

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

Cf. A100787, A210025.