[seqfan] Re: defn of A167415

[Don Reble]

> How is A167415 defined?

    It looks like,
    M such that (for all x,y except x=y=0) (x+y)^2+3xy isn't == 0 mod M.
    At any rate, this Python jot produces the sequence data.

#!/usr/bin/python3
for mod in range(2,300):
    halfmod = (mod // 2) + 1
    for x in range(halfmod):
        xsq = x * x
        for y in range(max(x,1),halfmod):
            sumsq = y * y + xsq
            xy3 = x * y * 3
            val = (sumsq + xy3) % mod
            if val == 0: break
            val = (sumsq - xy3) % mod
            if val == 0: break
        if val == 0: break
    if val != 0: print(mod)


> %C Prime numbers of this sequence are congruent to {2,3} modulo 5.

    BTW, that formula equals (x^2 + 5xy + y^2);
    that may be why modulo 5 matters.

-- 
Don Reble  djr at nk.ca