A365747 Decimal expansion of Trinv(1 + Trinv(2 + Trinv(3 + Trinv(4 + ... )))) where Trinv(n) = (sqrt(8*n+1)-1)/2.

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, 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, 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

Offset: 1

Author

Kelvin Voskuijl, Sep 17 2023

Keywords

• nonn
• cons

Comments

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

Examples

			2.2814374140534244152717727285916507607333884526610...
		

Crossrefs

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

Cf. A000217 (triangular numbers), A003056.

Programs

Mathematica

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