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
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Jun 22 2001
STATUS
approved