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 A062397 a(n) = 10^n+1. 33

%I

%S 2,11,101,1001,10001,100001,1000001,10000001,100000001,1000000001,

%T 10000000001,100000000001,1000000000001,10000000000001,

%U 100000000000001,1000000000000001,10000000000000001,100000000000000001

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

%H Vincenzo Librandi, <a href="/A062397/b062397.txt">Table of n, a(n) for n = 0..200</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 = A011557(n)+1 = A002283(n)+2

%F G.f.: 1/(1-x)+1/(1-10*x). E.g.f.: exp(x)+exp(10*x). - _Mohammad K. Azarian_, Jan 02 2009

%t LinearRecurrence[{11, -10},{2, 11},18] (* _Ray Chandler_, Aug 26 2015 *)

%o (MAGMA) [10^n + 1: n in [0..35]]; // _Vincenzo Librandi_, Apr 30 2011

%o (PARI) a(n)=10^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Except for the initial term, essentially the same as A000533. Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600-A074624, A034524, A178248, A228081 for numbers one more than powers, i.e. this sequence translated from base n(>2) to base 10.

%K easy,nonn

%O 0,1

%A _Henry Bottomley_, Jun 22 2001

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