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
Dana Jacobsen, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 17 2016
EXTENSIONS
Terms a(21) and beyond from Dana Jacobsen, Aug 18 2016
STATUS
approved