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.
1, 1, 2, 5, 11, 4, 3, 18, 26, 35, 48, 66, 16, 99, 129, 27, 67, 149, 190, 8, 235, 259, 285, 348, 276, 34, 24, 97, 362, 170, 155, 15, 504, 464, 9, 639, 449, 173, 391, 768, 577, 682, 836, 937, 598, 438, 94, 6, 1063, 1007, 500, 210, 1146, 1303, 1390, 806, 1530, 62, 1096, 1739, 212, 28, 1001, 1380
Offset: 1
Keywords
Examples
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.
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..600
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