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A325077
Prime numbers congruent to 4, 10 or 25 modulo 39 representable by x^2 + x*y + 10*y^2.
3
43, 103, 181, 277, 439, 673, 751, 823, 1039, 1063, 1117, 1429, 1453, 1759, 1993, 1999, 2131, 2287, 2311, 2467, 2521, 2539, 2617, 2833, 2851, 2857, 3067, 3163, 3457, 3559, 3613, 3637, 3847, 3943, 4021, 4027, 4177, 4261, 4339, 4723, 4783, 4861, 5113, 5119, 5197
OFFSET
1,1
COMMENTS
Brink showed that prime numbers congruent to 4, 10 or 25 modulo 39 are representable by exactly one of the quadratic forms x^2 + x*y + 10*y^2 or x^2 + x*y + 127*y^2. This sequence corresponds to those representable by the first form, and A325078 corresponds to those representable by the second form.
LINKS
David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.
EXAMPLE
Regarding 43:
- 43 is a prime number,
- 43 = 39 + 4,
- 43 = 1^2 + 1*2 + 10*2^2,
- hence 43 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
See A325067 for similar results.
Cf. A325078.
Sequence in context: A033227 A106888 A142795 * A023293 A115606 A194773
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 28 2019
STATUS
approved