A249119 Decimal expansion of Product_{k >= 0} 1+1/(2^(2^k)+1).

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

Offset

1,2

Comments

This number is irrational.

References

Michal Křížek, Florian Luca and Lawrence Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, Springer-Verlag, 2001, p. 110.

Links

Table of n, a(n) for n=1..105.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 247.

Vladimir Shevelev, On Stephan's conjectures concerning Pascal triangle modulo 2, arXiv:1011.6083 [math.NT] (2012).

Wikipedia, Fermat number

Formula

Equals Sum_{k>=0} 1/A001317(k). - Amiram Eldar, Aug 28 2019

Example

1.700735495286404851307357433922232663183172213974564676846046458482861...

Prog

(Magma) c:=[&*[1+1/(2^(2^k)+1): k in [0..8]]][1]; Reverse(Intseq(Floor(10^104*c)));
(PARI) prodinf(k=0, 1+1/(2^(2^k)+1)) \\ Michel Marcus, Oct 21 2014

Crossrefs

Cf. A000215, A001317.

Sequence in context: A132712 A021592 A235140 * A154102 A344785 A240984

Adjacent sequences: A249116 A249117 A249118 * A249120 A249121 A249122

Keyword

nonn,cons,easy,changed

Author

Arkadiusz Wesolowski, Oct 21 2014

Status

approved