

A327743


a(n) = smallest positive number not already in the sequence such that for each k = 1, ..., n1, the kth differences are distinct.


9



1, 2, 4, 3, 6, 11, 5, 9, 7, 13, 10, 18, 8, 15, 27, 14, 23, 12, 22, 17, 28, 16, 29, 20, 34, 19, 35, 21, 36, 32, 24, 42, 26, 43, 25, 44, 66, 33, 53, 30, 51, 31, 54, 37, 61, 39, 64, 38, 67, 40, 70, 41, 68, 47, 75, 50, 76, 45, 77, 49, 80, 48, 81, 46, 82, 52, 86
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OFFSET

1,2


COMMENTS

Is this sequence a permutation of the positive integers?
Does each kth difference contain all nonzero integers?
It is not difficult to show that if a(1), ..., a(k) satisfy the requirements, then any sufficiently large number is a candidate for a(k+1). So a(k) exists for all k.  N. J. A. Sloane, Sep 24 2019
The original definition was "Lexicographically earliest infinite sequence of distinct positive integers such that for every k >= 1, the kth differences are distinct."
If only first differences are considered, one gets the classical MianChowla sequence A005282.  M. F. Hasler, Oct 09 2019


LINKS

Peter Kagey, Table of n, a(n) for n = 1..5000


EXAMPLE

Illustration of the first eight terms of the sequence.
k  kth differences
+
0  1, 2, 4, 3, 6, 11, 5, 9
1  1, 2, 1, 3, 5, 6, 4
2  1, 3, 4, 2, 11, 10
3  4, 7, 2, 13, 21
4  11, 9, 11, 34
5  20, 2, 45
6  18, 47
7  29


MATHEMATICA

a[1] = 1;
a[n_] := a[n] = For[aa = Array[a, n1]; an = 1, True, an++, If[FreeQ[aa, an], aa = Append[aa, an]; If[AllTrue[Range[n1], Unequal @@ Differences[ aa, #]&], Return[an]]]];
a /@ Range[1, 100] (* JeanFrançois Alcover, Oct 26 2019 *)


CROSSREFS

Cf. A175498.
First differences: A327452; leading column of difference triangle: A327457.
If ALL terms of the difference triangle must be distinct, see A327460 and A327762.
Cf. A005282.
Sequence in context: A285493 A064273 A257986 * A232564 A134561 A258046
Adjacent sequences: A327740 A327741 A327742 * A327744 A327745 A327746


KEYWORD

nonn,nice


AUTHOR

Peter Kagey, Sep 24 2019


EXTENSIONS

"Infinite" added to definition (for otherwise the oneterm sequence 1 is earlier).  N. J. A. Sloane, Sep 25 2019
Changed definition to avoid use of "Lexicographically earliest infinite sequence" and the associated existence questions.  N. J. A. Sloane, Sep 28 2019


STATUS

approved



