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A363554 a(1) = 1; for n > 1, a(n) is the smallest positive integer such that both the gradients and y-intercepts of the lines between any two points (i, a(i)) and (j, a(j)) are distinct.

%I A363554 #11 Jul 03 2023 09:16:58
%S A363554 1,1,2,5,11,4,3,18,26,35,48,66,16,99,129,27,67,149,190,8,235,259,285,
%T A363554 348,276,34,24,97,362,170,155,15,504,464,9,639,449,173,391,768,577,
%U A363554 682,836,937,598,438,94,6,1063,1007,500,210,1146,1303,1390,806,1530,62,1096,1739,212,28,1001,1380
%N A363554 a(1) = 1; for n > 1, a(n) is the smallest positive integer such that both the gradients and y-intercepts of the lines between any two points (i, a(i)) and (j, a(j)) are distinct.
%C A363554 This is a variation of A286091 where the y-intercepts of all lines are also distinct.
%H A363554 Scott R. Shannon, <a href="/A363554/b363554.txt">Table of n, a(n) for n = 1..600</a>
%e A363554 a(12) = 66. A value of 15, with coordinate (12,15), for this term would create a point for which all line gradients are distinct, see A286091, but it creates a line that passes through the origin with a(4), a point with coordinate (4,5). However the terms a(3), at coordinate (3,2) and a(6), at coordinate (6,4), have already created a line that passes through the origin, thus a(12) cannot be 15. The coordinate (12,66) is the first point the leads to all lines and y-intercepts being distinct.
%Y A363554 Cf. A286091, A236335, A229037.
%K A363554 nonn
%O A363554 1,3
%A A363554 _Scott R. Shannon_, Jun 10 2023