A306980 Decimal expansion of the sum of the reciprocals of the star numbers (A003154).

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

Offset: 1

Author

Amiram Eldar, Mar 18 2019

Keywords

• nonn
• cons

Examples

			1.15917331963217469507856662406743787684463551195593...
		

Crossrefs

Cf. A003154, A093766 (Pi/(2*sqrt(3))).

Programs

Mathematica

s[n_]:=6*n*(n-1) + 1; RealDigits[Sum[1/s[n], {n,1,Infinity}], 10, 100][[1]]

Formula

Equals Sum_{n>=1} 1/(6*n*(n-1) + 1) = x * tan(x) with x = Pi/(2*sqrt(3)).