login
A371649
Decimal expansion of Sum_{k>=0} 1/Lucas(5^k).
2
1, 0, 9, 0, 9, 1, 5, 0, 5, 1, 7, 7, 0, 0, 7, 7, 6, 7, 0, 0, 1, 8, 6, 5, 7, 5, 0, 2, 4, 1, 4, 2, 2, 8, 2, 0, 5, 7, 1, 5, 1, 7, 5, 1, 0, 2, 3, 1, 9, 9, 0, 6, 6, 9, 8, 9, 0, 5, 0, 3, 2, 1, 7, 0, 9, 2, 2, 2, 4, 3, 0, 8, 1, 7, 5, 8, 2, 8, 8, 4, 4, 6, 4, 9, 0, 2, 6, 3, 1, 9, 6, 7, 3, 7, 2, 4, 8, 1, 8, 3, 1, 2, 4, 1, 7
OFFSET
1,3
COMMENTS
This constant is a transcendental number (Nyblom, 2001).
LINKS
M. A. Nyblom, A Theorem on Transcendence of Infinite Series II, Journal of Number Theory, Vol. 91, No. 1 (2001), pp. 71-80.
FORMULA
Equals Sum_{k>=0} 1/A144837(k).
EXAMPLE
1.09091505177007767001865750241422820571517510231990...
MATHEMATICA
RealDigits[Sum[1/LucasL[5^k], {k, 0, 10}], 10, 120][[1]]
PROG
(PARI) suminf(k = 0, 1/(fibonacci(5^k-1) + fibonacci(5^k+1)))
CROSSREFS
Similar constants: A093540, A338304, A338612, A371647.
Sequence in context: A372947 A010680 A248724 * A278144 A198220 A131566
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 31 2024
STATUS
approved