A306968 Numbers prime to 7 that are not represented by x^2+y^2+7*z^2.

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

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): 341-345.

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 (* Jean-François 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(m-7*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