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A275878
Standard Jacobi primes.
3
7, 61, 331, 547, 1951, 2437, 3571, 4219, 7351, 8269, 9241, 10267, 13669, 23497, 25117, 55897, 60919, 74419, 89269, 92401, 102121, 112327, 115837, 126691, 145861, 170647, 202021, 231019, 241117, 246247, 251431, 267307, 283669, 329677, 347821, 360187, 372769
OFFSET
1,1
COMMENTS
From Peter Bala, Feb 20 2022: (Start)
Primes of the form (3*k + 2)^3 - (3*k + 1)^3 = 27*k^2 + 27*k + 7.
Equivalently, primes p such that 4*p = 27*x^2 + 1, where x is odd.
Primes p of the form 6*m + 1, where 8*m + 1 is an odd square.
A prime p is in this list iff binomial(2*(p-1)/3,(p-1)/3) == -1 (mod p). See Cosgrave and Dilcher, Theorem 5, Corollary 3. (End)
Subsequence of cuban primes (A002407). - Bernard Schott, Jul 28 2022
LINKS
John B. Cosgrave and Karl Dilcher, An Introduction to Gauss Factorials, Amer. Math. Monthly, Vol. 118, No. 9 (November 2011), pp. 812-829.
J. B. Cosgrave and Karl Dilcher, A role for generalized Fermat numbers, Math. Comp., to appear 2016; see also Paper #10, See Table 7.1.
PROG
(Perl) use ntheory ":all"; forprimes { if (($_%3)==1) { my $z = znorder(factorial(($_-1)/3), $_); $z/=3 unless $z%3; say if $z==1; } } 1e6; # Dana Jacobsen, Aug 18 2016
(Perl) use ntheory ":all"; for (0..1000) { my $p = 27*$_*$_ + 27*$_ + 7; say $p if is_prime($p); } # Dana Jacobsen, Aug 18 2016
CROSSREFS
Sequence in context: A141952 A289723 A064398 * A129079 A249556 A135165
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 17 2016
EXTENSIONS
Terms a(21) and beyond from Dana Jacobsen, Aug 18 2016
STATUS
approved