1,1

The constant is equal to lim_{n -> oo} A190020(n)/A190019(n), which is the ratio of the probability of an obtuse triangle to an acute triangle, when all three vertices are drawn uniformly at random in a square.

Table of n, a(n) for n=1..105.

Code Golf Stack Exchange, Ratio of obtuse triangles to acute triangles in the square.

Eric Langford, The probability that a random triangle is obtuse, Biometrika, 56(3), 1969, p. 689.

Plot of A190020(n)/A190019(n) vs n using OEIS Plot2.

2.6390960417866483205308889755825371915092...

RealDigits[(388 + 15*Pi)/(212 - 15*Pi), 10, 100][[1]]

(PARI) (388 + 15*Pi)/(212 - 15*Pi) \\ Michel Marcus, Feb 25 2021

Cf. A000796, A190019, A190020.

Sequence in context: A082154 A134564 A016637 * A133917 A229760 A078340

Adjacent sequences: A341939 A341940 A341941 * A341943 A341944 A341945

nonn,cons

Peter Kagey, Feb 24 2021

approved