A371647 Decimal expansion of Sum_{k>=0} 1/Fibonacci(5^k).

1, 2, 0, 0, 0, 1, 3, 3, 2, 8, 8, 9, 0, 3, 6, 9, 8, 7, 6, 7, 0, 7, 7, 6, 4, 0, 9, 5, 4, 6, 8, 3, 5, 5, 0, 5, 6, 4, 3, 0, 5, 5, 5, 0, 6, 8, 8, 1, 3, 8, 0, 2, 6, 5, 7, 3, 0, 3, 6, 6, 1, 3, 7, 9, 4, 6, 9, 2, 6, 5, 6, 7, 8, 8, 5, 6, 9, 4, 8, 2, 4, 6, 2, 8, 6, 7, 7, 2, 7, 9, 4, 3, 4, 7, 6, 7, 4, 1, 0, 9, 0, 7, 0, 6, 2

Offset: 1

Author

Amiram Eldar, Mar 31 2024

Keywords

• nonn
• cons

Comments

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

Examples

			1.20001332889036987670776409546835505643055506881380...
		

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. A000045, A145232, A371648.

Similar constants: A079585, A079586, A153386, A153387, A371649.

Programs

Mathematica

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

PARI

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

Formula

Equals Sum_{k>=0} 1/A145232(k).