|
Search: id:A014663
|
|
|
| A014663 |
|
Primes p such that order of 2 mod p is odd. |
|
+0
5
|
|
| 7, 23, 31, 47, 71, 73, 79, 89, 103, 127, 151, 167, 191, 199, 223, 233, 239, 263, 271, 311, 337, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 601, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 881, 887
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Or, primes p which do not divide 2^n+1 for any n.
The possibility n=0 in the above rules out A072936(1)=2; apart from this, A014663(n)=A072936(n+1). - M. F. Hasler, Dec 08 2007
The order of 2 mod p is odd iff 2^k=1 mod p, where p-1=2^s*k, k odd. - M. F. Hasler, Dec 08 2007
|
|
REFERENCES
|
H. H. Hasse, Ueber die Dichte der Primzahlen p, ..., Math. Ann., 168 (1966), 19-23.
J. C. Lagarias, The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math., 118 (1985), 449-461.
P. Moree, Appendix to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
|
|
FORMULA
|
Has density 7/24 (Hasse)
|
|
PROGRAM
|
(PARI) isA014663(p)=1==Mod(1, p)<<((p-1)>>factor(p-1, 2)[1, 2]) listA014663(N=1000)=forprime(p=3, N, isA014663(p)&print1(p", ")) \\ - M. F. Hasler, Dec 08 2007
|
|
CROSSREFS
|
Cf. Complement in primes of A091317.
Cf. A040098, A045315, A049564.
Cf. Essentially the same as A072936 (except for missing leading term 2).
Sequence in context: A036259 A004628 A089199 this_sequence A141175 A007522 A157811
Adjacent sequences: A014660 A014661 A014662 this_sequence A014664 A014665 A014666
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Edited by M. F. Hasler (maximilian.hasler(AT)gmail.com), Dec 08 2007
|
|
|
Search completed in 0.002 seconds
|
