|
| |
| |
|
|
|
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; 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 sequences related to linear recurrences with constant coefficients
|
|
|
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 (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
E.g.f.: e^x+e^(8*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 02 2009]
|
|
|
MATHEMATICA
| Table[8^n + 1, {n, 0, 20}]
|
|
|
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 for numbers one more than powers.
Sequence in context: A152915 A168383 A071300 * A099975 A127056 A042255
Adjacent sequences: A062392 A062393 A062394 * A062396 A062397 A062398
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 22 2001
|
| |
|
|
