

A129805


Primes congruent to +1 mod 18.


13



17, 19, 37, 53, 71, 73, 89, 107, 109, 127, 163, 179, 181, 197, 199, 233, 251, 269, 271, 307, 359, 379, 397, 431, 433, 449, 467, 487, 503, 521, 523, 541, 557, 577, 593, 613, 631, 647, 683, 701, 719, 739, 757, 773, 809, 811, 827, 829, 863, 881, 883, 919, 937, 953, 971, 991
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OFFSET

1,1


COMMENTS

Equivalently, primes p such that the smallest extension of F_p containing the cube roots of unity also contains the 9th roots of unity.
Equivalently, the primes p for which, if p^t = 1 mod 3, then p^t = 1 mod 9.
Equivalently, primes congruent to +/1 modulo 9.
Membership or nonmembership of the prime p in this sequence and sequence A002144 (primes congruent to 1 mod 4; equivalently, primes p such that the smallest extension of F_p containing the square roots of unity contains the 4th roots of unity) appear to determine the behavior of amicable pairs on the elliptic curve y^2 = x^3 + p (Silverman, Stange 2009). (End)
Equivalently, primes such that p^2 == 1 (mod 9).  M. F. Hasler, Apr 16 2022


LINKS



MATHEMATICA

Select[Prime[Range[4000]], MemberQ[{1, 17}, Mod[#, 18]]&] (* Vincenzo Librandi, Aug 14 2012 *)


PROG

(Haskell)
a129805 n = a129805_list !! (n1)
a129805_list = [x  x < a056020_list, a010051 x == 1]
(Magma) [ p: p in PrimesUpTo(1300)  p mod 18 in {1, 17} ]; // Vincenzo Librandi, Aug 14 2012


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



