login
Decimal expansion of 2*(1+sqrt(10))/3.
4

%I #33 May 23 2021 15:37:43

%S 2,7,7,4,8,5,1,7,7,3,4,4,5,5,8,6,2,2,1,3,3,2,5,9,5,6,9,6,2,8,8,4,7,9,

%T 0,2,2,4,7,9,7,0,3,4,2,6,2,1,6,8,1,1,2,1,7,9,0,5,0,0,3,2,3,5,1,9,5,0,

%U 6,2,9,5,9,0,9,2,8,2,5,4,8,0,8,9,6,1,6,5,4,0,5,5,8,6

%N Decimal expansion of 2*(1+sqrt(10))/3.

%C Trisect the unit square into 3 regions with equal areas from a given midpoint on the squares edge. This sequence gives the decimal expansion of the perimeter of the triangular region.

%F Decimal expansion of 2*(1 + k*sqrt(1/k^2 + 1))/k, where k = 3.

%e 2.7748517734455862213325956962884790...

%t RealDigits[2 (1 + Sqrt[10])/3, 10, 200][[1]] // Flatten

%Y Similar sequences into k regions: A344554 (k=5), A343069 (k=7), A344568 (k=9), A344569 (k=17).

%K nonn,cons

%O 1,1

%A _Wesley Ivan Hurt_, May 22 2021