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A062395 a(n) = 8^n + 1. 49
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
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
Sequence in context: A152915 A168383 A071300 * A352986 A099975 A292976
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Jun 22 2001
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)