A371323 - OEIS

%I #7 Mar 19 2024 10:28:49

%S 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,

%T 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,

%U 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

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

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

%H M. A. Nyblom, <a href="https://doi.org/10.1006/jnth.2001.2672">A Theorem on Transcendence of Infinite Series II</a>, Journal of Number Theory, Vol. 91, No. 1 (2001), pp. 71-80.

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

%e 0.59027838058250762481004953440302226140463948387293...

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

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

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 19 2024