%I #13 Jul 28 2025 08:43:49

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

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

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

%N Decimal expansion of 1/(2*cosh(1)^2).

%H Hideyuki Ohtsuka, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.124.5.465">Problem 11978</a>, Problems and Solutions, The American Mathematical Monthly, Vol. 124, No. 5 (2017), p. 465; <a href="https://www.jstor.org/stable/48662488">A Sum of Hyperbolic Cosines of Fibonacci Numbers</a>, Solution to Problem 11978 by Kyle Gatesman, ibid., Vol. 126, No. 2 (2019), p. 185.

%F Equals 1/(2*A073743^2).

%F Equals Sum_{n>=0} (-1)^n/(cosh(Fibonacci(n)) * cosh(Fibonacci(n+3))) (Ohtsuka, 2017).

%e 0.20998717080701303469724836952085072245859336411538...

%t RealDigits[1/(2*Cosh[1]^2), 10, 120][[1]]

%o (PARI) 1/(2*cosh(1)^2)

%Y Cf. A000045, A073743.

%K nonn,cons,easy

%O 0,1

%A _Amiram Eldar_, Jul 25 2025