A371323 Decimal expansion of Sum_{k>=1} 1/(2^k * Lucas(k!)).

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

Offset

0,1

Comments

The transcendence of this constant was proved by Nyblom (2001).

Links

Table of n, a(n) for n=0..104.

M. A. Nyblom, A Theorem on Transcendence of Infinite Series II, Journal of Number Theory, Vol. 91, No. 1 (2001), pp. 71-80.

Index entries for transcendental numbers.

Example

0.59027838058250762481004953440302226140463948387293...

Mathematica

RealDigits[Sum[1/(2^k * LucasL[k!]), {k, 1, 10}], 10, 120][[1]]

Prog

(PARI) suminf(k = 1, 1/(2^k * (fibonacci(k!-1)+fibonacci(k!+1))))

Crossrefs

Cf. A000032, A000142, A101293, A343202, A371322, A371324, A371325.

Sequence in context: A344966 A294613 A144408 * A019636 A269979 A102521

Adjacent sequences: A371320 A371321 A371322 * A371324 A371325 A371326

Keyword

nonn,cons

Author

Amiram Eldar, Mar 19 2024

Status

approved