|
|
A030433
|
|
Primes of form 10*k + 9.
|
|
49
|
|
|
19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619, 659, 709, 719, 739, 769, 809, 829, 839, 859, 919, 929, 1009, 1019, 1039, 1049, 1069, 1109, 1129, 1229, 1249, 1259, 1279, 1289
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Also primes of form 5*k + 4.
Conjecture: Primes p such that ((x+1)^5-1)/x has 2 distinct irreducible factors of degree 2 over GF(p). - Federico Provvedi, Apr 01 2018
The digital root of a(n) is 1, 2, 4, 5, 7 or 8. - Muniru A Asiru, Apr 28 2018
Primes p such that the ideal (p) factors into two prime ideals in Z[zeta_5], where zeta_5 = exp(2*Pi*i/5). Since Z[zeta_5] is a PID, this is equivalent to saying that this sequence lists primes p that are the product of two non-associate prime elements Z[zeta_5]. In particular, the factorization of p == 4 (mod 5) in Z[zeta_5] coincides with the factorization in Z[(1+sqrt(5))/2] (e.g., 19 = (8+3*sqrt(5))*(8-3*sqrt(5)) is the factorization of 19 in both Z[(1+sqrt(5))/2] and Z[zeta_5]).
Also primes p such that x^4 + x^3 + x^2 + x + 1 factors into two irreducible quadratic polynomials over GF(p) (cf. A327753). (End)
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
select(isprime, [seq(10*n+9, n=1..500)]); # Muniru A Asiru, Apr 27 2018
|
|
MATHEMATICA
|
Select[Prime@Range[210], Mod[ #, 10] == 9 &] (* Ray Chandler, Nov 07 2006 *)
Prime@Flatten@Position[Length@FactorList[((1+d)^5-1)/d, Modulus->#]&/@Prime@Range@200, 3] (* Federico Provvedi, Apr 04 2018 *)
|
|
PROG
|
(PARI) for(n=1, 1e3, if(isprime(p=10*n+9), print1(p, ", "))); \\ Altug Alkan, Apr 19 2018
(GAP) Filtered(List([1..500], n->10*n+9), IsPrime); # Muniru A Asiru, Apr 27 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|