%I #29 Sep 08 2022 08:45:03
%S 2,9,65,513,4097,32769,262145,2097153,16777217,134217729,1073741825,
%T 8589934593,68719476737,549755813889,4398046511105,35184372088833,
%U 281474976710657,2251799813685249,18014398509481985,144115188075855873
%N a(n) = 8^n + 1.
%C Any number of the form b^k+1 is composite for b>2 and k odd since b+1 algebraically divides b^k+1. - _Robert G. Wilson v_, Aug 25 2002
%D D. M. Burton, Elementary Number Theory, Allyn and Bacon, Boston, MA, 1976, pp. 51.
%D G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%H Vincenzo Librandi, <a href="/A062395/b062395.txt">Table of n, a(n) for n = 0..140</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F a(n) = 8a(n-1)-7 = A001018(n)+1 = 9a(n-1) - 8a(n-2).
%F G.f.: -(-2+9*x)/(-1+x)/(-1+8*x). - _R. J. Mathar_, Nov 16 2007
%F E.g.f.: e^x+e^(8*x). - _Mohammad K. Azarian_, Jan 02 2009
%t Table[8^n + 1, {n, 0, 20}]
%t LinearRecurrence[{9,-8},{2,9},20] (* _Harvey P. Dale_, Jan 24 2019 *)
%o (PARI) for(n=0,22,print(8^n+1)).
%o (Magma) [8^n + 1: n in [0..40] ]; // _Vincenzo Librandi_, Apr 30 2011
%Y Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, A062396, A062397, A007689, A063376, A063481, A074600 - A074624, A034524, A178248, A228081 for numbers one more than powers.
%K easy,nonn
%O 0,1
%A _Henry Bottomley_, Jun 22 2001