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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 Table of n, a(n) for n=1..56. 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 Cf. A327743, A327460. 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 Adjacent sequences: A327759 A327760 A327761 * A327763 A327764 A327765 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.)