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Decimal expansion of 2*(1+sqrt(82))/9.
4

%I #9 May 23 2021 15:37:53

%S 2,2,3,4,5,3,0,0,3,0,6,9,7,2,0,3,6,9,4,7,9,4,1,7,9,5,9,2,6,6,3,1,2,5,

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

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

%N Decimal expansion of 2*(1+sqrt(82))/9.

%C Dissect the unit square into 9 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 with unit height.

%F Decimal expansion of 2*(1 + k*sqrt(1/k^2 + 1))/k, where k = 9.

%e 2.2345300306972036947941795926631...

%t RealDigits[2 (1 + Sqrt[82])/9, 10, 200][[1]] // Flatten

%Y Similar sequences into k regions: A344520 (k=3), A344554 (k=5), A343069 (k=7), A344569 (k=17).

%K nonn,cons

%O 1,1

%A _Wesley Ivan Hurt_, May 23 2021