A101690 Decimal expansion of the unique real number x whose Engel expansion is the Lucas sequence.

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

Offset: 1

Author

Ryan Propper, Dec 11 2004

Keywords

• cons
• nonn

Examples

			x = 1.4297159226892042002772306926271655374969467995845816636429774710...
		

Crossrefs

Cf. A101689, A000204.

Programs

Mathematica

Lucas[n_Integer?Positive] := Lucas[n] = Lucas[n-1] + Lucas[n-2]; Lucas[1] = 1; Lucas[2] = 3; N[Sum[1/Product[Lucas[i], {i, n}], {n, 500}], 100]
digits = 100; Clear[x]; x[m_] := x[m] = N[Sum[1/Product[LucasL[i], {i, 1, n}], {n, 1, m}], digits+5]; m = 10; While[x[m] != x[m-1], m++]; RealDigits[x[m], 10, digits][[1]] (* Jean-François Alcover, Nov 20 2015 *)

Formula

x = Sum_{n >= 1} 1/(Product_{1 <= i <= n} L(i)), where L(i) is the i-th Lucas number.

Extensions

Offset corrected by Amiram Eldar, Nov 09 2020