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%I #12 Sep 08 2022 08:45:30
%S 9,119,1329,14639,161049,1771559,19487169,214358879,2357947689,
%T 25937424599,285311670609,3138428376719,34522712143929,
%U 379749833583239,4177248169415649,45949729863572159,505447028499293769
%N a(n) = 11^n - 2.
%C There are only two known primes in a(n): a(4) = 14639 and a(6) = 1771559 (see A128472 = smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists. 3 divides a(2k-1). 7 divides a(3k-1). 13 divides a(12k-5). 17 divides a(16k-14).
%C Final digit of a(n) is 9.
%C Final two digits of a(n) are periodic with period 10: a(n) mod 100 = {09, 19, 29, 39, 49, 59, 69, 79, 89, 99}.
%C Final three digits of a(n) are periodic with period 50: a(n) mod 1000 = {009, 119, 329, 639, 049, 559, 169, 879, 689, 599, 609, 719, 929, 239, 649, 159, 769, 479, 289, 199, 209, 319, 529, 839, 249, 759, 369, 079, 889, 799, 809, 919, 129, 439, 849, 359, 969, 679, 489, 399, 409, 519, 729, 039, 449, 959, 569, 279, 089, 999}.
%H Vincenzo Librandi, <a href="/A130652/b130652.txt">Table of n, a(n) for n = 1..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12, -11).
%F a(n) = 11*a(n-1) + 20; a(1)=9. - _Vincenzo Librandi_, Jun 08 2011
%t LinearRecurrence[{12, -11},{9, 119},17] (* _Ray Chandler_, Aug 26 2015 *)
%o (Magma) [11^n - 2: n in [1..50]]; // _Vincenzo Librandi_, Jun 08 2011
%Y Cf. A001020, A024127, A034524. Cf. A104096 = Largest prime <= 11^n. Cf. A084714 = smallest prime of the form (2n-1)^k - 2, or 0 if no such number exists. Cf. A128472 = smallest prime of the form (2n-1)^k - 2 for k>(2n-1), or 0 if no such number exists. Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Jun 20 2007
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