A381110 a(n) is the maximum number of points from the set {(k, f(k)); k = 0..n} belonging to a straight line passing through the point (n, f(n)), where f(n) = A060143(n) = floor(n/phi) and phi is the golden ratio (sqrt(5)+1)/2.

1, 2, 2, 2, 3, 3, 4, 3, 5, 3, 4, 4, 4, 5, 3, 5, 4, 4, 6, 4, 5, 5, 5, 6, 5, 6, 7, 6, 5, 6, 7, 6, 7, 5, 7, 8, 6, 8, 6, 7, 9, 6, 9, 7, 6, 10, 6, 7, 8, 7, 11, 7, 7, 9, 7, 12, 7, 8, 10, 8, 8, 8, 8, 11, 8, 9, 9, 9, 9, 8, 9, 10, 9, 10, 9, 10, 11, 8, 10, 10, 10, 11, 8

Offset

0,2

Comments

The sequence would remain the same if A060143 in the definition were replaced with A066096, i.e., if points (k, floor(k*phi)) were considered instead of (k, floor(k/phi)).

Links

Pontus von Brömssen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A060143, A066096, A375422, A381111.

Sequence in context: A155216 A064144 A338295 * A271519 A077105 A173752

Adjacent sequences: A381107 A381108 A381109 * A381111 A381112 A381113

Keyword

nonn,look

Author

Pontus von Brömssen, Feb 14 2025

Status

approved