A371137 - OEIS

%I #6 Mar 12 2024 02:47:04

%S 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,

%T 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,

%U 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

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

%C Nyblom (2000) proved that this constant is transcendental.

%H M. A. Nyblom, <a href="https://doi.org/10.1216/rmjm/1021477261">A theorem on transcendence of infinite series</a>, The Rocky Mountain Journal of Mathematics, Vol. 30, No. 3 (2000), pp. 1111-1120; <a href="https://www.jstor.org/stable/44238526">alternative link</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

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

%e 1.38889853376456644140523703662326084973849454043352...

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

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

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

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, Mar 12 2024