Search: id:A062395
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%I A062395
%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 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 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%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 (mathar(AT)strw.leidenuniv.nl), 
               Nov 16 2007
%F A062395 E.g.f.: e^x+e^(8*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Jan 02 2009]
%p A062395 with(finance):seq(mul(cashflows([2,2,4], 0 ),k=1..n)+1,n=0..19); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
%t A062395 Table[8^n + 1, {n, 0, 20}]
%o A062395 (PARI) for(n=0,22,print(8^n+1)).
%Y A062395 Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, 
               A062396, A062397, A007689, A063376, A063481, A074600 - A074624, A034524 
               for numbers one more than powers.
%Y A062395 Sequence in context: A048801 A152915 A071300 this_sequence A099975 A127056 
               A042255
%Y A062395 Adjacent sequences: A062392 A062393 A062394 this_sequence A062396 A062397 
               A062398
%K A062395 easy,nonn
%O A062395 0,1
%A A062395 Henry Bottomley (se16(AT)btinternet.com), Jun 22 2001

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