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A371325
Decimal expansion of Sum_{k>=1} (-1)^(k+1)/(2^k * Lucas(k!)).
3
4, 2, 3, 6, 1, 0, 5, 0, 8, 3, 0, 6, 3, 8, 1, 2, 6, 4, 0, 7, 8, 8, 3, 9, 3, 5, 9, 7, 0, 2, 1, 7, 4, 1, 5, 5, 3, 3, 6, 7, 2, 6, 6, 9, 9, 2, 6, 8, 7, 2, 6, 0, 6, 1, 7, 4, 0, 4, 6, 6, 9, 1, 7, 4, 7, 4, 7, 6, 6, 9, 2, 0, 9, 3, 4, 9, 4, 7, 9, 7, 1, 2, 8, 4, 9, 2, 3, 5, 7, 9, 1, 3, 7, 3, 4, 6, 1, 1, 5, 2, 3, 9, 9, 4, 5
OFFSET
0,1
COMMENTS
The transcendence of this constant was proved by Nyblom (2004).
LINKS
M. A. Nyblom, An extension of a result of SierpiƄski, Journal of Number Theory, Vol. 105, No. 1 (2004), pp. 49-59.
EXAMPLE
0.42361050830638126407883935970217415533672669926872...
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)))
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 19 2024
STATUS
approved