A309361 Numbers n such that the number of interior intersection points A091908(n) of the n-intersected triangle increases exactly by 1 when the subdivision of the triangle is refined from n-1 to n cutting line segments.

1, 3, 5, 7, 9, 11, 13, 17, 21, 25, 27, 31, 33, 37, 43, 49, 51, 53, 55, 57, 61, 67, 73, 81, 93, 97, 101, 107, 113, 115, 121, 123, 127, 133, 137, 141, 145, 147, 157, 163, 173, 177, 183, 185, 193, 201, 205, 211, 213, 217, 235, 241, 243, 249, 253, 257

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Hugo Pfoertner, Illustration of a(2)=3, A091908(3)=A091908(4)-1.

Formula

A091908(a(n) + 1) = A091908(a(n)) + 1.

Example

a(1) = 1 corresponds to change from the triangle without cutting line segments and correspondingly A091908(1)=0 interior intersection points to the triangle where the sides are divided into 2 equal pieces and the 3 line segments connecting the midpoints of the sides with the opposite vertices cutting each other in one common point, the center of gravity. (A091908(2)=1). Thus A091908(2) - A091908(1) = 1 -> a(1) = 1.
a(2) = 3 because the trisected triangle has one less interior intersection point (A091908(3) = 12) than the 4-sected triangle (A091908(4) = 13) -> a(2) = 3.

Crossrefs

Cf. A091908, A092098, A309360.

Sequence in context: A358975 A345898 A172095 * A133854 A239008 A291343

Adjacent sequences: A309358 A309359 A309360 * A309362 A309363 A309364

Keyword

nonn

Author

Hugo Pfoertner, Jul 26 2019

Status

approved