%I #27 Nov 26 2023 04:13:42

%S 3,21,201,2001,20001,200001,2000001,20000001,200000001,2000000001,

%T 20000000001,200000000001,2000000000001,20000000000001,

%U 200000000000001,2000000000000001,20000000000000001,200000000000000001,2000000000000000001

%N a(n) = 2*10^n + 1.

%C Numbers k such that (R(k) - 1)/(k + 1) = 1/2, where R(k) denotes the digit reversal of k (cf. A004086). - _Stefano Spezia_, Nov 25 2023

%H Vincenzo Librandi, <a href="/A199682/b199682.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = 10*a(n-1)-9.

%F a(n) = 11*a(n-1)-10*a(n-2).

%F G.f.: 3*(1-4*x)/((1-x)*(1-10*x)).

%F E.g.f.: 2*exp(10*x) + exp(x). - _Stefano Spezia_, Nov 25 2023

%t NestList[10#-9&,3,20] (* or *) LinearRecurrence[{11,-10},{3,21},20] (* _Harvey P. Dale_, Sep 30 2017 *)

%o (Magma) [2*10^n+1: n in [0..30]];

%o (Haskell)

%o a199682 = (+ 1) . (* 2) . (10 ^) -- _Reinhard Zumkeller_, Jan 30 2015

%o (PARI) a(n)=2*10^n+1 \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A004086, A011557, A133384.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 09 2011