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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.

%I A309361 #9 Aug 13 2019 08:46:28
%S A309361 1,3,5,7,9,11,13,17,21,25,27,31,33,37,43,49,51,53,55,57,61,67,73,81,
%T A309361 93,97,101,107,113,115,121,123,127,133,137,141,145,147,157,163,173,
%U A309361 177,183,185,193,201,205,211,213,217,235,241,243,249,253,257
%N 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.
%H A309361 Hugo Pfoertner, <a href="/A309361/a309361.pdf">Illustration of a(2)=3</a>, A091908(3)=A091908(4)-1.
%F A309361 A091908(a(n) + 1) = A091908(a(n)) + 1.
%e A309361 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.
%e A309361 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.
%Y A309361 Cf. A091908, A092098, A309360.
%K A309361 nonn
%O A309361 1,2
%A A309361 _Hugo Pfoertner_, Jul 26 2019