A393801 - OEIS

%I #8 May 18 2026 22:00:14

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

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

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

%N Decimal expansion of 1 - 2/sqrt(5).

%C This constant gives the linear asymptotic coefficient of the average number of hairpins in an RNA secondary structure on a number n of vertices tending to infinity (see Theorem 3 in Bu, Kauers, and Zeilberger).

%H AJ Bu, Manuel Kauers, and Doron Zeilberger, <a href="https://arxiv.org/abs/2602.19255">Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures</a>, arXiv:2602.19255 [math.CO], 2026.

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

%F Minimal polynomial: 5*x^2 - 10*x + 1.

%e 0.105572809000084121436330532507489505823752656155...

%t RealDigits[1-2/Sqrt[5],10,100][[1]]

%o (PARI) 1-2/sqrt(5) \\ _Charles R Greathouse IV_, May 18 2026

%Y Cf. A002163, A010532, A393800, A393802.

%K nonn,cons,easy

%O 0,3

%A _Stefano Spezia_, Feb 27 2026