|
Search: id:A091317
|
|
|
| A091317 |
|
Primes p which divide 2^n+1 for some n. |
|
+0
3
|
|
| 2, 3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 83, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419, 421, 433
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Contribution from Charles R Greathouse IV Feb 13 2009): (Start)
Essentially the same as A014662.
Also primes p for which p^2 divides 2^n+1 for some n. If p | 2^g + 1, then 2^g = kp - 1 for some k, so 2^gp = (kp - 1)^p = (-1)^p + (-1)^(p-1) * kp * (p choose 1) + ... and so 2^gp = -1 (mod p^2). (End)
|
|
REFERENCES
|
H. H. Hasse, Ueber die Dichte der Primzahlen p, ..., Math. Ann., 168 (1966), 19-23.
L. C. Lagarias, The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math., 118 (1985), 449-461.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
|
|
FORMULA
|
Has density 17/24 (Hasse)
|
|
PROGRAM
|
(PARI) isA091317(p)=!bitand(znorder(Mod(2, p)), 1) [From Charles R Greathouse IV Feb 13 2009]
|
|
CROSSREFS
|
Complement in primes of A014663.
Cf. A014662 [From Charles R Greathouse IV Feb 13 2009]
Sequence in context: A126148 A038933 A042998 this_sequence A088254 A089191 A038947
Adjacent sequences: A091314 A091315 A091316 this_sequence A091318 A091319 A091320
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Feb 21 2004
|
|
EXTENSIONS
|
Comments and program from Charles R Greathouse IV Feb 13 2009
|
|
|
Search completed in 0.002 seconds
|
