login
a(n) = (10^n + 17)/9.
4

%I #18 Aug 23 2024 12:47:32

%S 2,3,13,113,1113,11113,111113,1111113,11111113,111111113,1111111113,

%T 11111111113,111111111113,1111111111113,11111111111113,

%U 111111111111113,1111111111111113,11111111111111113,111111111111111113,1111111111111111113,11111111111111111113,111111111111111111113

%N a(n) = (10^n + 17)/9.

%C A097683 gives numbers k such that a(k) is prime.

%H Ivan Panchenko, <a href="/A098406/b098406.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(1) = 3; a(n) = a(n-1) + 10^(n-1).

%F a(1) = 3; a(n) = 10*a(n-1) - 17.

%F a(n) = A047855(n)+1 = A002275(n)+2.

%F G.f.: (2-19*x)/((10*x-1)*(x-1)). - _R. J. Mathar_, Jan 27 2017

%F From _Elmo R. Oliveira_, Aug 23 2024: (Start)

%F E.g.f.: exp(x)*(exp(9*x) + 17)/9.

%F a(n) = A062397(n) - A002282(n).

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

%e a(5) = (100000 + 17)/9 = 11113.

%t FromDigits/@Table[PadLeft[{3},n,1],{n,20}] (* _Harvey P. Dale_, Jun 18 2011 *)

%o (PARI) for(n=1,18,print1(((10^n)+17)/9,","))

%Y Cf. A097683, A047855, A002275.

%Y Cf. A002282, A062397.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Sep 07 2004

%E a(0) from _Ivan Panchenko_, Nov 02 2013