A107905 Decimal expansion of (5+sqrt(21))/2.

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

Offset: 1

Author

Jonathan Vos Post, Jun 22 2007

Keywords

• cons
• easy
• nonn

Examples

			4.7912878474779200032940235968640042444922282883839859513036...
The zeros at 15, 16 and 17 digits after the decimal point allow for a good rational approximation. The continued fraction is [4,1,3,1,3,1,3,...] = 4 + 1/(1+ 1/(3+ 1/(1+ 1/(3+ 1/(1+ 1/(3+ 1(/1+ ...
		

References

• D. Mumford et al., Indra's Pearls, Cambridge 2002; see p. 317. [From N. J. A. Sloane, Nov 22 2009]

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
• Emma Y. Jin and Christian M. Reidys, Asymptotic Enumeration of RNA Structures with Pseudoknots, arXiv:0706.3137 [q-bio.BM], 2007, Theorem 5, p. 15.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Equals 1+A090458. - R. J. Mathar, Aug 24 2008

Cf. A004253, A004254.

Programs

Mathematica

RealDigits[(5+Sqrt[21])/2,10,120][[1]] (* Harvey P. Dale, May 02 2011 *)

PARI

(sqrt(21)+5)/2 \\ Charles R Greathouse IV, Feb 11 2025

Formula

(4.791287...)^n = A090458 * A004254(n) + A004253(n). - Gary W. Adamson, Sep 11 2023

Equals lim_{n->oo} S(n, 5)/S(n-1, 5), with the S-Chebyshev polynomial (see A049310) S(n, 5) = A004254(n+1). - Wolfdieter Lang, Nov 15 2023

c^k = A004254(k)*c - A004254(k-1) for k >= 1, where c is the present constant. - Andrea Pinos, Jul 19 2024

Minimal polynomial: x^2 - 5*x + 1. - Stefano Spezia, Jul 02 2025