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A101690
Decimal expansion of the unique real number x whose Engel expansion is the Lucas sequence.
1
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
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
Sequence in context: A257734 A257732 A351164 * A213781 A257730 A246378
KEYWORD
cons,nonn
AUTHOR
Ryan Propper, Dec 11 2004
EXTENSIONS
Offset corrected by Amiram Eldar, Nov 09 2020
STATUS
approved