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A325072
Prime numbers congruent to 1 modulo 20 neither representable by x^2 + 20*y^2 nor by x^2 + 100*y^2.
3
41, 61, 241, 281, 421, 601, 641, 661, 701, 821, 881, 1181, 1201, 1301, 1321, 1381, 1481, 1801, 1901, 2141, 2161, 2221, 2281, 2341, 2381, 2521, 2741, 3041, 3061, 3181, 3221, 3361, 3541, 3701, 3761, 4241, 4261, 4421, 4481, 4721, 4801, 5381, 5501, 5521, 5581
OFFSET
1,1
COMMENTS
Brink showed that prime numbers congruent to 1 modulo 20 are representable by both or neither of the quadratic forms x^2 + 20*y^2 and x^2 + 100*y^2. A325071 corresponds to those representable by both, and this sequence corresponds to those representable by neither.
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 2221:
- 2221 is a prime number,
- 2221 = 111*20 + 1,
- 2221 is neither representable by x^2 + 20*y^2 nor by x^2 + 100*y^2,
- hence 2221 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
See A325067 for similar results.
Sequence in context: A195573 A260554 A031415 * A089345 A320468 A055110
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 27 2019
STATUS
approved