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3*10^n+1.
4

%I #19 Sep 08 2022 08:46:00

%S 4,31,301,3001,30001,300001,3000001,30000001,300000001,3000000001,

%T 30000000001,300000000001,3000000000001,30000000000001,

%U 300000000000001,3000000000000001,30000000000000001,300000000000000001,3000000000000000001

%N 3*10^n+1.

%H Vincenzo Librandi, <a href="/A199683/b199683.txt">Table of n, a(n) for n = 0..1000</a>

%H S. W. Golomb, <a href="http://www.jstor.org/stable/2005337">Properties of the sequence 3.2^n+1</a>, Math. Comp., 30 (1976), 657-663.

%H S. W. Golomb, <a href="/A004119/a004119.pdf">Properties of the sequence 3.2^n+1</a>, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]

%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.: (4-13*x)/((1-x)*(1-10*x)).

%t 3*10^Range[0,20]+1 (* or *) LinearRecurrence[{11,-10},{4,31},20] (* _Harvey P. Dale_, Dec 12 2016 *)

%o (Magma) [3*10^n+1: n in [0..30]];

%Y Primes: A056807, A259866.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 09 2011