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%I #24 Sep 08 2022 08:44:48
%S 1,10,119,1328,14637,161046,1771555,19487164,214358873,2357947682,
%T 25937424591,285311670600,3138428376709,34522712143918,
%U 379749833583227,4177248169415636,45949729863572145,505447028499293754
%N a(n) = 11^n - n.
%C Smallest prime of this form is a(18) = 5559917313492231463. - _Bruno Berselli_, Jun 17 2013
%H Vincenzo Librandi, <a href="/A024128/b024128.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-23,11).
%F G.f.: (1-3*x+12*x^2)/((1-11*x) (1-x)^2). - _Vincenzo Librandi_, Jun 17 2013
%F a(n) = 13*a(n-1) - 23*a(n-2) + 11*a(n-3). - _Vincenzo Librandi_, Jun 17 2013
%t Table[11^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 12 x^2) / ((1 - 11 x) (1 - x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 17 2013 *)
%t LinearRecurrence[{13,-23,11},{1,10,119},20] (* _Harvey P. Dale_, Aug 02 2017 *)
%o (Magma) [11^n-n: n in [0..20]]; // _Vincenzo Librandi_, Jul 01 2011
%o (PARI) a(n)=11^n-n \\ _Charles R Greathouse IV_, Jul 01 2011
%o (Magma) I:=[1, 10, 119]; [n le 3 select I[n] else 13*Self(n-1)-23*Self(n-2)+11*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 17 2013
%Y Cf. numbers of the form k^n-n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), this sequence (k=11), A024141 (k=12).
%Y Cf. A199030 (first differences).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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