A363554 - OEIS

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 #11 Jul 03 2023 09:16:58

%S 1,1,2,5,11,4,3,18,26,35,48,66,16,99,129,27,67,149,190,8,235,259,285,

%T 348,276,34,24,97,362,170,155,15,504,464,9,639,449,173,391,768,577,

%U 682,836,937,598,438,94,6,1063,1007,500,210,1146,1303,1390,806,1530,62,1096,1739,212,28,1001,1380

%N 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 This is a variation of A286091 where the y-intercepts of all lines are also distinct.

%H Scott R. Shannon, <a href="/A363554/b363554.txt">Table of n, a(n) for n = 1..600</a>

%e 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 Cf. A286091, A236335, A229037.

%K nonn

%O 1,3

%A _Scott R. Shannon_, Jun 10 2023