A393801 Decimal expansion of 1 - 2/sqrt(5).

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, 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, 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

Offset

0,3

Comments

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).

Links

Table of n, a(n) for n=0..99.

AJ Bu, Manuel Kauers, and Doron Zeilberger, Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures, arXiv:2602.19255 [math.CO], 2026.

Index entries for algebraic numbers, degree 2.

Formula

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

Example

0.105572809000084121436330532507489505823752656155...

Mathematica

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

Prog

(PARI) 1-2/sqrt(5) \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A002163, A010532, A393800, A393802.

Sequence in context: A226571 A274030 A061382 * A113272 A388829 A222392

Adjacent sequences: A393798 A393799 A393800 * A393802 A393803 A393804

Keyword

nonn,cons,easy

Author

Stefano Spezia, Feb 27 2026

Status

approved