OFFSET
1,2
COMMENTS
Each row begins with 1. For example, the 12th row is for N=13. The numbers in that row are 1, 9, 17, 25, 29 and 49, which means that the primes represented by the quadratic form x^2+13y^2 (A033210) are congruent to 1, 9, 17, 25, 29,or 49 (mod 52). Cox lists some of these congruences on page 36 of his book. As mentioned by Cox, for these N, every term of the congruence has the form b^2 or N+b^2 for some integer b. In some cases, the congruences can be simplified. For instance, for N=18 (A106950), the congruence is 1, 19, 25, 43, 49, 67 (mod 72), which can be simplified to 1, 19 (mod 24).
REFERENCES
David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, Section 3.
LINKS
T. D. Noe, Rows n=1..65 of triangle, flattened
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
EXAMPLE
1, 2,
1, 2, 3,
1, 3, 7,
1, 5, 9, 13,
1, 5, 9,
1, 7,
1, 7, 9, 11, 15, 23, 25,
1, 9, 17, 25,
1, 13, 25,
1, 9, 11, 19,
1, 13, 25, 37,
1, 9, 13, 17, 25, 29, 49,
1, 19, 31, 49,
1, 9, 17, 25, 33, 41, 49, 57,
1, 19, 25, 43, 49, 67,
1, 25, 37,
1, 9, 15, 23, 25, 31, 47, 49, 71, 81,
1, 25, 49, 73,
...
CROSSREFS
KEYWORD
fini,nonn,tabf
AUTHOR
T. D. Noe, Apr 28 2008
STATUS
approved