|
|
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
|
|
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)).
|
|
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.
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|