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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}]

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 A127056 A228696

Adjacent sequences:  A062392 A062393 A062394 * A062396 A062397 A062398

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Jun 22 2001

STATUS

approved

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Last modified May 22 19:31 EDT 2017. Contains 286885 sequences.