

A306968


Numbers prime to 7 that are not represented by x^2+y^2+7*z^2.


0



3, 6, 19, 22, 31, 51, 55, 66, 94, 139, 142, 159, 166, 214, 235, 283, 439, 534, 559, 670, 874, 946, 1726, 2131, 2419, 3559, 4759
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OFFSET

1,1


COMMENTS

If it exists, a(28) > 10^7.  Andrew Howroyd, Aug 17 2019


LINKS

Table of n, a(n) for n=1..27.
Irving Kaplansky, The first nontrivial genus of positive definite ternary forms, Mathematics of Computation, Vol. 64 (1995): 341345.


MATHEMATICA

max = 10000;
Table[Table[Table[x^2 + y^2 + 7 z^2, {z, 0, Sqrt[max  x^2  y^2]/Sqrt[7] // Ceiling}], {y, 0, Sqrt[max  x^2] // Ceiling}], {x, 0, Sqrt[max] // Ceiling}] // Flatten // Union // Select[#, # <= max&]& // Complement[ Select[ Range[max], CoprimeQ[#, 7]&], #]& // Quiet (* JeanFrançois Alcover, Aug 27 2019 *)


PROG

(PARI)
issumsquare(n)={my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return(0))); 1}
ok(m)={if(m%7, for(i=0, sqrtint(m\7), if(issumsquare(m7*i^2), return(0))); 1, 0)}
select(ok, [1..10000]) \\ Andrew Howroyd, Aug 17 2019


CROSSREFS

Cf. A097633.
Sequence in context: A085401 A085061 A294570 * A090956 A108972 A304965
Adjacent sequences: A306965 A306966 A306967 * A306969 A306970 A306971


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Mar 26 2019


STATUS

approved



