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A129805
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Primes congruent to +-1 mod 18.
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13
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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
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1,1
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COMMENTS
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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 non-membership 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
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LINKS
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MATHEMATICA
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Select[Prime[Range[4000]], MemberQ[{1, 17}, Mod[#, 18]]&] (* Vincenzo Librandi, Aug 14 2012 *)
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PROG
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(Haskell)
a129805 n = a129805_list !! (n-1)
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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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