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

Author

Hugo Pfoertner, Jul 26 2019

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A091908, A092098, A309360.

Formula

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