OFFSET
1,1
COMMENTS
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, a(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
Has density 7/24 (Hasse).
REFERENCES
Christopher Adler and Jean-Paul Allouche (2022), Finite self-similar sequences, permutation cycles, and music composition, Journal of Mathematics and the Arts, 16:3, 244-261, DOI: 10.1080/17513472.2022.2116745.
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
H. H. Hasse, Über 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. No. 2, (1985), 449-461.
Chunlei Li, Nian Li, and Matthew G. Parker, Complementary Sequence Pairs of Types II and III. [From N. J. A. Sloane, Jun 16 2012]
MATHEMATICA
okQ[p_] := OddQ[MultiplicativeOrder[2, p]];
Select[Prime[Range[1000]], okQ] (* Jean-François Alcover, Nov 23 2024 *)
PROG
(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
(PARI) lista(nn) = {forprime(p=3, nn, if (znorder(Mod(2, p)) % 2, print1(p, ", ")); ); } \\ Michel Marcus, Feb 06 2015
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
N. J. A. Sloane, Dec 11 1999.
EXTENSIONS
Edited by M. F. Hasler, Dec 08 2007
More terms from Max Alekseyev, Feb 06 2010
STATUS
approved