OFFSET
1,1
COMMENTS
Also primes congruent to {1, 9, 15, 23, 25, 39} mod 56.
From Wolfdieter Lang, Jun 04 2021: (Start)
Discriminant -8*7. The product of two entries is congrunet to {1, 7} (mod 8). Buell, p. 51, 3).
The given two reduced positive definite binary quadratic forms represent the odd primes, not 7, with the generic characters Legendre(p|7) = +1 and Legendre(2|p) = +1. The other two reduced forms are [3, 2, 5] and [3,-2, 5] with values -1 and -1 for these two generic characters, and give the odd primes, not 7, listed in A106915. This is related to the two genera of discriminant -56 with class number h(-56) = 4. See Buell, p. 52, 2), and Cox, p. 30.
There is a misprint 29 (instead of 39) in Cox (1989, ISBN 0-471-50654-0), p. 33, in eqs. (2.21) and 2.23). (End)
In the first US edition, there just one error, in Eq. (2.21), and it is on page 33. In the second edition this error has been corrected. - N. J. A. Sloane, Jun 04 2021
REFERENCES
D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 51-53.
David A. Cox, Primes of the Form x^2 + n y^2, John Wiley & Sons, 1st edition, 1989; 2nd edition, 2003.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Thomas R. Hagedorn, Primes of the form x^2+ny^2 and the geometry of (convenient) numbers (page 3).
MATHEMATICA
Select[Prime@Range[300], MemberQ[{1, 9, 15, 23, 25, 39}, Mod[#, 56]] &]
PROG
(Magma) [p: p in PrimesUpTo(3000) | p mod 56 in {1, 9, 15, 23, 25, 39} ];
(PARI) is(n) = ispseudoprime(n) && #setintersect([n % 56], [1, 9, 15, 23, 25, 39])==1 \\ Felix Fröhlich, Jul 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jul 02 2016
STATUS
approved