|
|
A020515
|
|
a(n) = 4^n - 2^n + 1.
|
|
14
|
|
|
1, 3, 13, 57, 241, 993, 4033, 16257, 65281, 261633, 1047553, 4192257, 16773121, 67100673, 268419073, 1073709057, 4294901761, 17179738113, 68719214593, 274877382657, 1099510579201
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
6th cyclotomic polynomial evaluated at powers of 2.
Referred to as Kasami-Welch numbers by Aubry et al. (see links). The first prime values are a(1) = 3, a(2) = 13, a(4) = 241, a(32) = 18446744069414584321, no more for n less than or equal to 100. - Jonathan Vos Post, Sep 15 2009
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(1-4*x) - 1/(1-2*x) + 1/(1-x).
E.g.f.: e^(4*x) - e^(2*x) + e^x. (End)
|
|
MAPLE
|
with(numtheory, cyclotomic):seq(cyclotomic(6, 2**i), i=0..24);
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|