This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A062395 a(n) = 8^n + 1. 44
 2, 9, 65, 513, 4097, 32769, 262145, 2097153, 16777217, 134217729, 1073741825, 8589934593, 68719476737, 549755813889, 4398046511105, 35184372088833, 281474976710657, 2251799813685249, 18014398509481985, 144115188075855873 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 REFERENCES D. M. Burton, Elementary Number Theory, Allyn and Bacon, Boston, MA, 1976, pp. 51. G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..140 Index entries for linear recurrences with constant coefficients, signature (9,-8). FORMULA a(n) = 8a(n-1)-7 = A001018(n)+1 = 9a(n-1) - 8a(n-2). G.f.: -(-2+9*x)/(-1+x)/(-1+8*x). - R. J. Mathar, Nov 16 2007 E.g.f.: e^x+e^(8*x). - Mohammad K. Azarian, Jan 02 2009 MATHEMATICA Table[8^n + 1, {n, 0, 20}] LinearRecurrence[{9, -8}, {2, 9}, 20] (* Harvey P. Dale, Jan 24 2019 *) PROG (PARI) for(n=0, 22, print(8^n+1)). (MAGMA) [8^n + 1: n in [0..40] ]; // Vincenzo Librandi, Apr 30 2011 CROSSREFS 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. Sequence in context: A152915 A168383 A071300 * A099975 A292976 A127056 Adjacent sequences:  A062392 A062393 A062394 * A062396 A062397 A062398 KEYWORD easy,nonn AUTHOR Henry Bottomley, Jun 22 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)