This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A062395 #32 Jan 23 2025 20:06:26
%S A062395 2,9,65,513,4097,32769,262145,2097153,16777217,134217729,1073741825,
%T A062395 8589934593,68719476737,549755813889,4398046511105,35184372088833,
%U A062395 281474976710657,2251799813685249,18014398509481985,144115188075855873
%N A062395 a(n) = 8^n + 1.
%C A062395 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 A062395 D. M. Burton, Elementary Number Theory, Allyn and Bacon, Boston, MA, 1976, pp. 51.
%D A062395 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%H A062395 Vincenzo Librandi, <a href="/A062395/b062395.txt">Table of n, a(n) for n = 0..140</a>
%H A062395 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F A062395 a(n) = 8a(n-1)-7 = A001018(n)+1 = 9a(n-1) - 8a(n-2).
%F A062395 G.f.: -(-2+9*x)/(-1+x)/(-1+8*x). - _R. J. Mathar_, Nov 16 2007
%F A062395 E.g.f.: e^x+e^(8*x). - _Mohammad K. Azarian_, Jan 02 2009
%t A062395 Table[8^n + 1, {n, 0, 20}]
%t A062395 LinearRecurrence[{9,-8},{2,9},20] (* _Harvey P. Dale_, Jan 24 2019 *)
%o A062395 (PARI) for(n=0,22,print(8^n+1))
%o A062395 (Magma) [8^n + 1: n in [0..40] ]; // _Vincenzo Librandi_, Apr 30 2011
%Y A062395 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 A062395 easy,nonn
%O A062395 0,1
%A A062395 _Henry Bottomley_, Jun 22 2001