cp's OEIS Frontend

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.

%I A327762 #55 Aug 14 2025 04:25:13
%S A327762 1,3,9,5,12,10,23,8,22,17,42,16,43,20,38,26,45,32,65,28,64,39,76,34,
%T A327762 81,48,98,40,92,54,109,60,116,51,114,58,117,70,136,67,135,71,145,72,
%U A327762 147,69,146,80,164,87,166,82,170,108,198,99
%N 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.
%C A327762 Inspired by A327743.
%C A327762 From _Rémy Sigrist_, Sep 25 2019: (Start)
%C A327762 The sequence is finite, with 56 terms.
%C A327762 Let b and c be the first and second differences of a, respectively, hence:
%C A327762 - b(55) = a(56) - a(55) = 99 - 198 = -99,
%C A327762 - b(56) = a(57) - a(56) = a(57) - 99,
%C A327762 - c(55) = b(56) - b(55) = a(57), a contradiction.
%C A327762 (End)
%C A327762 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.
%C A327762 If only first differences are considered, one gets the classical Mian-Chowla sequence A005282. - _M. F. Hasler_, Oct 09 2019
%e A327762 Difference triangle of the first k=8 terms of the sequence:
%e A327762   1, 3, 9, 5, 12, 10, 23, 8, ...
%e A327762   2, 6, -4, 7, -2, 13, -15, ...
%e A327762   4, -10, 11, -9, 15, -28, ...
%e A327762   -14, 21, -20, 24, -43, ...
%e A327762   35, -41, 44, -67, ...
%e A327762   -76, 85, -111, ...
%e A327762   161, -196, ...
%e A327762   -357, ...
%e A327762 All 8*9/2 = 36 numbers are distinct.
%Y A327762 Cf. A327743, A327460.
%Y A327762 For first differences see A327458; for the leading column of the difference triangle see A327459.
%Y A327762 Cf. A005282.
%K A327762 nonn,full,fini
%O A327762 1,2
%A A327762 _N. J. A. Sloane_, Sep 24 2019, revised Sep 25 2019