A334363 - OEIS

%I #16 Apr 05 2024 08:17:40

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

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

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

%N Decimal expansion of Sum_{k>=0} 1/(4*k+1)!.

%H Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2011). See p. 36.

%F Equals (sin(1) + sinh(1))/2.

%e 1/1! + 1/5! + 1/9! + ... = 1.008336089225848981767442...

%t RealDigits[(Sin[1] + Sinh[1])/2, 10, 110] [[1]]

%o (PARI) suminf(k=0, 1/(4*k+1)!) \\ _Michel Marcus_, Apr 25 2020

%Y Cf. A001113, A049469, A073742, A143820, A332890, A334364, A334365.

%K nonn,cons

%O 1,4

%A _Ilya Gutkovskiy_, Apr 24 2020