cp's OEIS Frontend

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

%I A107905 #47 Jul 02 2025 10:59:41
%S A107905 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,
%T A107905 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,
%U A107905 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
%N A107905 Decimal expansion of (5+sqrt(21))/2.
%D A107905 D. Mumford et al., Indra's Pearls, Cambridge 2002; see p. 317. [From _N. J. A. Sloane_, Nov 22 2009]
%H A107905 Daniel Starodubtsev, <a href="/A107905/b107905.txt">Table of n, a(n) for n = 1..10000</a>
%H A107905 Emma Y. Jin and Christian M. Reidys, <a href="http://arxiv.org/abs/0706.3137">Asymptotic Enumeration of RNA Structures with Pseudoknots</a>, arXiv:0706.3137 [q-bio.BM], 2007, Theorem 5, p. 15.
%H A107905 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A107905 (4.791287...)^n = A090458 * A004254(n) + A004253(n). - _Gary W. Adamson_, Sep 11 2023
%F A107905 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
%F A107905 c^k = A004254(k)*c - A004254(k-1) for k >= 1, where c is the present constant. - _Andrea Pinos_, Jul 19 2024
%F A107905 Minimal polynomial: x^2 - 5*x + 1. - _Stefano Spezia_, Jul 02 2025
%e A107905 4.7912878474779200032940235968640042444922282883839859513036...
%e A107905 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+ ...
%t A107905 RealDigits[(5+Sqrt[21])/2,10,120][[1]] (* _Harvey P. Dale_, May 02 2011 *)
%o A107905 (PARI) (sqrt(21)+5)/2 \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A107905 Equals 1+A090458. - _R. J. Mathar_, Aug 24 2008
%Y A107905 Cf. A004253, A004254.
%K A107905 cons,easy,nonn
%O A107905 1,1
%A A107905 _Jonathan Vos Post_, Jun 22 2007