A343202 Decimal expansion of Sum_{k>=0} 1/(k! * Fibonacci(2^k)).

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

Offset

1,1

Comments

The transcendence of this constant was proved independently by Mignotte (1974) and Mahler (1975).

References

Maurice Mignotte, Quelques problèmes d'effectivité en théorie des nombres, Thesis, Univ. Paris XIII, Paris, 1974.

Links

Table of n, a(n) for n=1..100.

Kurt Mahler, On the transcendency of the solutions of a special class of functional equations, Bulletin of the Australian Mathematical Society, Vol. 13, No. 3 (1975), pp. 389-410.

Example

2.17464539389651955644333792522982188971668174552838...

Mathematica

RealDigits[Sum[1/(n!*Fibonacci[2^n]), {n, 0, 20}], 10, 100][[1]]

Prog

(PARI) suminf(k=0, 1/(k!*fibonacci(2^k))) \\ Michel Marcus, Jul 07 2021

Crossrefs

Cf. A000045, A000142, A058635, A079585.

Sequence in context: A107865 A089225 A185110 * A075085 A217458 A124048

Adjacent sequences: A343199 A343200 A343201 * A343203 A343204 A343205

Keyword

nonn,cons

Author

Amiram Eldar, Jul 07 2021

Status

approved