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

1,3

Comments

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

Links

Scott R. Shannon, Table of n, a(n) for n = 1..600

Example

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.

Crossrefs

Cf. A286091, A236335, A229037.

Sequence in context: A175311 A246208 A286091 * A127011 A170868 A357588

Adjacent sequences: A363551 A363552 A363553 * A363555 A363556 A363557

Keyword

nonn

Author

Scott R. Shannon, Jun 10 2023

Status

approved