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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
Inspired by A327743.
From Rémy Sigrist, Sep 25 2019: (Begin)
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 Mian-Chowla 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.
Cf. A005282.
Sequence in context: A223652 A077383 A084492 * A327460 A084496 A084530
KEYWORD
nonn,full,fini
AUTHOR
N. J. A. Sloane, Sep 24 2019, revised Sep 25 2019.
STATUS
approved

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Last modified May 18 18:37 EDT 2024. Contains 372664 sequences. (Running on oeis4.)