A371649 Decimal expansion of Sum_{k>=0} 1/Lucas(5^k).

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

Author

Amiram Eldar, Mar 31 2024

Keywords

• nonn
• cons

Comments

This constant is a transcendental number (Nyblom, 2001).

Examples

			1.09091505177007767001865750241422820571517510231990...
		

Links

• 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.

Crossrefs

Cf. A000032, A144837, A371650.

Similar constants: A093540, A338304, A338612, A371647.

Programs

Mathematica

RealDigits[Sum[1/LucasL[5^k], {k, 0, 10}], 10, 120][[1]]

PARI

suminf(k = 0, 1/(fibonacci(5^k-1) + fibonacci(5^k+1)))

Formula

Equals Sum_{k>=0} 1/A144837(k).