A365747 - OEIS

%I #16 Dec 06 2023 14:25:09

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

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

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

%N Decimal expansion of Trinv(1 + Trinv(2 + Trinv(3 + Trinv(4 + ... )))) where Trinv(n) = (sqrt(8*n+1)-1)/2.

%C Trinv(n) = (sqrt(8*n+1)-1)/2 is the inverse of A000217.

%e 2.2814374140534244152717727285916507607333884526610...

%t TriangleRoot[n_] =(-1 + Sqrt[1 + 8 n])/2; RealDigits[ Fold[ TriangleRoot[ #1 + #2] &, 0, Reverse[ Range[200]]], 10,111][[1]]

%Y Cf. A072449 (analog for square root), A099874 (analog for cube root).

%Y Cf. A000217 (triangular numbers), A003056.

%K nonn,cons

%O 1,1

%A _Kelvin Voskuijl_, Sep 17 2023