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

1,2

Links

Table of n, a(n) for n=1..100.

Formula

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

Example

x = 1.4297159226892042002772306926271655374969467995845816636429774710...

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 *)

Crossrefs

Cf. A101689, A000204.

Sequence in context: A257734 A257732 A351164 * A213781 A257730 A246378

Adjacent sequences: A101687 A101688 A101689 * A101691 A101692 A101693

Keyword

cons,nonn

Author

Ryan Propper, Dec 11 2004

Extensions

Offset corrected by Amiram Eldar, Nov 09 2020

Status

approved