cp's OEIS Frontend

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

%I A249119 #37 Feb 23 2025 21:51:28
%S A249119 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,
%T A249119 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,
%U A249119 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
%N A249119 Decimal expansion of Product_{k >= 0} 1+1/(2^(2^k)+1).
%C A249119 This number is irrational.
%D A249119 Michal Křížek, Florian Luca and Lawrence Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, Springer-Verlag, 2001, p. 110.
%H A249119 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 247.
%H A249119 Vladimir Shevelev, <a href="https://arxiv.org/abs/1011.6083">On Stephan's conjectures concerning Pascal triangle modulo 2</a>, arXiv:1011.6083 [math.NT] (2012).
%H A249119 Wikipedia, <a href="http://en.wikipedia.org/wiki/Fermat_number">Fermat number</a>
%F A249119 Equals Sum_{k>=0} 1/A001317(k). - _Amiram Eldar_, Aug 28 2019
%F A249119 Equals Sum_{i>=0} A079559(i)/2^i. - _Jwalin Bhatt_, Feb 09 2025
%e A249119 1.700735495286404851307357433922232663183172213974564676846046458482861...
%o A249119 (Magma) c:=[&*[1+1/(2^(2^k)+1): k in [0..8]]][1]; Reverse(Intseq(Floor(10^104*c)));
%o A249119 (PARI) prodinf(k=0, 1+1/(2^(2^k)+1)) \\ _Michel Marcus_, Oct 21 2014
%Y A249119 Cf. A000215, A001317, A380373, A079559 (binary expansion).
%K A249119 nonn,cons,easy
%O A249119 1,2
%A A249119 _Arkadiusz Wesolowski_, Oct 21 2014