A394915 Consider the following process: at step n, draw the line passing through the points (n, prime(n)) and (n+1, prime(n+1)). a(n) gives the total number of distinct single-point line intersections after step n.

0, 1, 1, 3, 5, 8, 11, 15, 22, 25, 31, 31, 37, 37, 46, 46, 51, 59, 59, 67, 76, 76, 87, 104, 115, 125, 137, 150, 165, 186, 202, 219, 234, 259, 275, 292, 292, 315, 334, 334, 355, 387, 407, 432, 451, 488, 488, 511, 532, 560, 584, 609, 646, 646, 646, 646, 672, 698, 725, 755, 796, 844

Offset

1,4

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Paolo Xausa, Illustration of a(10) = 25

Paolo Xausa, Illustration of a(50) = 560

Paolo Xausa, Illustration of a(100) = 2327

Mathematica

A394915list[nmax_] := Module[{lines = MapIndexed[{#2[[1]], #} &, Partition[Prime[Range[nmax+1]], 2, 1]], pts = {}, int}, int[{x1_, {y1_, y2_}}, {x3_, {y3_, y4_}}] := If[# == 0, Nothing, With[{a = x3*y4 - y3*(x3 + 1), b = x1*y2 - y1*(x1 + 1)}, {(a - b)/#, (b*(y3 - y4) - a*(y1 - y2))/#}]] & [y1 - y2 - y3 + y4]; Table[Length[pts = DeleteDuplicates[Join[pts, Map[int[#, lines[[n]]] &, lines[[;; n-1]]]]]], {n, nmax}]];
A394915list[100]

Crossrefs

Partial sums of A394225.

Cf. A373813, A375422.

Sequence in context: A228848 A049706 A080415 * A340318 A175489 A289244

Adjacent sequences: A394912 A394913 A394914 * A394916 A394917 A394918

Keyword

nonn

Author

Paolo Xausa, Apr 09 2026

Status

approved