A010695 - OEIS

%I #60 Jan 16 2025 06:34:33

%S 2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,

%T 2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,

%U 2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5

%N Period 2: repeat (2,5).

%C Also decimal expansion of 25/99.

%C Continued fraction expansion of A176052. - _R. J. Mathar_, Mar 08 2012

%C Periodic part of the partial quotients of the continued fraction expansion of sqrt(7/5), which starts [1, 5, 2, 5, 2, 5, ...]. - _Hugo Pfoertner_, Jan 10 2025

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).

%F G.f.: (2+5*x)/((1-x)*(1+x)). - _R. J. Mathar_, Nov 21 2011

%F a(n) = 2^(1-(-1)^n) + 1. - _Bruno Berselli_, Dec 29 2015

%F From _Nicolas Bělohoubek_, Nov 11 2021: (Start)

%F a(n) = 10/a(n-1). See also A010691.

%F a(n) = 7 - a(n-1). See also A010702. (End)

%t PadRight[{}, 100, {2, 5}] (* _Paolo Xausa_, Jan 16 2025 *)

%o (Maxima) makelist(if evenp(n) then 2 else 5, n, 0, 80); /* _Martin Ettl_, Nov 09 2012 */

%o (Magma) &cat [[2,5]^^50]; // _Bruno Berselli_, Dec 29 2015

%Y Cf. A010674 (2^(1-(-1)^n) - 1).

%Y Cf. A010691.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.

%E Edited by _Bruno Berselli_, Dec 29 2015