A387917 - OEIS

%I #56 May 19 2026 23:04:48

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

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

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

%N Decimal expansion of 5*sqrt(5)/3.

%H Hideyuki Ohtsuka, <a href="https://doi.org/10.1080/00150517.2025.2567941">Problem B-1373</a>, Elementary problems and solutions, The Fibonacci Quarterly, Vol. 63, No. 4 (2025), p. 754.

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

%F Equals 5 * A208899.

%F Equals 100 / A344171.

%F Equals Product_{k>=3} ((Fibonacci(k)+1)/(Fibonacci(k)-1))^((-1)^(k*(k+1)/2)) (Ohtsuka, 2025).

%e 3.72677996249964949401528944788546039240103059935254...

%t RealDigits[5*Sqrt[5]/3, 10, 120][[1]]

%o (PARI) list(len) = my(q = (quadgen(125)*2-1)/3); digits(floor(10^len * q));

%Y Cf. A000045, A134976, A208899, A344171.

%K nonn,cons

%O 1,1

%A _Amiram Eldar_, Dec 16 2025