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

Author

Amiram Eldar, Jul 07 2021

Keywords

• nonn
• cons

Comments

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

Examples

			2.17464539389651955644333792522982188971668174552838...
		

References

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

Links

• 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.

Crossrefs

Cf. A000045, A000142, A058635, A079585.

Programs

Mathematica

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

PARI

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