

A327762


a(n) = smallest positive number not already in the sequence such that all n(n+1)/2 numbers in the triangle of differences of the first n terms are distinct.


4



1, 3, 9, 5, 12, 10, 23, 8, 22, 17, 42, 16, 43, 20, 38, 26, 45, 32, 65, 28, 64, 39, 76, 34, 81, 48, 98, 40, 92, 54, 109, 60, 116, 51, 114, 58, 117, 70, 136, 67, 135, 71, 145, 72, 147, 69, 146, 80, 164, 87, 166, 82, 170, 108, 198, 99
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The sequence is finite, with 56 terms.
Let b and c be the first and second differences of a, respectively, hence:
 b(55) = a(56)  a(55) = 99  198 = 99,
 b(56) = a(57)  a(56) = a(57)  99,
 c(55) = b(56)  b(55) = a(57), a contradiction.
(End)
Since this definition leads to a finite sequence, it is natural to ask instead for the "Lexicographically earliest infinite sequence of distinct positive integers such that for every k >= 1, all the k(k+1)/2 numbers in the triangle of differences of the first k terms are distinct." This is A327460.
If only first differences are considered, one gets the classical MianChowla sequence A005282.  M. F. Hasler, Oct 09 2019


LINKS



EXAMPLE

Difference triangle of the first k=8 terms of the sequence:
1, 3, 9, 5, 12, 10, 23, 8, ...
2, 6, 4, 7, 2, 13, 15, ...
4, 10, 11, 9, 15, 28, ...
14, 21, 20, 24, 43, ...
35, 41, 44, 67, ...
76, 85, 111, ...
161, 196, ...
357, ...
All 8*9/2 = 36 numbers are distinct.


CROSSREFS

For first differences see A327458; for the leading column of the difference triangle see A327459.


KEYWORD

nonn,full,fini


AUTHOR



STATUS

approved



