A371137 Decimal expansion of Sum_{k>=1} 1/Lucas(k!).

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

Offset

1,2

Comments

Nyblom (2000) proved that this constant is transcendental.

Links

Table of n, a(n) for n=1..105.

M. A. Nyblom, A theorem on transcendence of infinite series, The Rocky Mountain Journal of Mathematics, Vol. 30, No. 3 (2000), pp. 1111-1120; alternative link.

Index entries for transcendental numbers.

Formula

Equals Sum_{k>=1} 1/A101293(k).

Example

1.38889853376456644140523703662326084973849454043352...

Mathematica

RealDigits[Sum[1/LucasL[k!], {k, 1, 10}], 10, 120][[1]]

Prog

(PARI) suminf(k = 1, 1/(fibonacci(k!-1)+fibonacci(k!+1)))

Crossrefs

Cf. A000032, A000142, A101293, A343202, A371136.

Sequence in context: A288094 A131596 A332892 * A140975 A065481 A354222

Adjacent sequences: A371134 A371135 A371136 * A371138 A371139 A371140

Keyword

nonn,cons

Author

Amiram Eldar, Mar 12 2024

Status

approved