A306324 Decimal expansion of 2*Pi*tanh(sqrt(5/3)*Pi/2)/sqrt(15).

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

Offset: 1

Author

Ilya Gutkovskiy, Feb 07 2019

Keywords

• nonn
• cons

Comments

Decimal expansion of the sum of the reciprocals of the centered triangular numbers (A005448).

Examples

			1.56706513126405467758811157795995464399516007...
		

Links

• Eric Weisstein's World of Mathematics, Centered Triangular Number

Crossrefs

Cf. A005448, A226985, A228048 (decimal expansion of the sum of the reciprocals of the centered square numbers), A303658.

Programs

Mathematica

RealDigits[2 Pi Tanh[Sqrt[5/3] Pi/2]/Sqrt[15], 10, 120][[1]]

PARI

2*Pi*tanh(sqrt(5/3)*Pi/2)/sqrt(15) \\ Michel Marcus, Feb 08 2019

Formula

Equals Sum_{k>=1} 1/(3*k*(k - 1)/2 + 1).

Equals Sum_{k>=1} 1/A005448(k).