A306989 Numbers not of the form x^2+2*y^2+7*z^2.

5, 14, 20, 21, 35, 42, 70, 84, 91, 119, 133, 140, 158, 168, 182, 189, 217, 231, 238, 245, 266, 280, 287, 315, 329, 336, 364, 378, 385, 413, 427, 434, 462, 476, 483, 511, 518, 525, 532, 560, 574, 581, 609, 623, 630, 658, 672, 679, 686, 707, 721, 728, 756, 770

Offset

1,1

Comments

It appears that the only terms not divisible by 7 are 5, 29 and 158. - Robert Israel, Mar 27 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Irving Kaplansky, The first nontrivial genus of positive definite ternary forms, Mathematics of Computation, Vol. 64 (1995): 341-345.

Maple

N:= 1000: # for terms <= N
V:= Array(0..N):
for x from 0 to floor(sqrt(N)) do
  for y from 0 to floor(sqrt((N-x^2)/2)) do
      for z from 0 do
      v:= x^2 + 2*y^2 + 7*z^2;
      if v > N then break fi;
      V[v]:= 1;
od od od:
select(t -> V[t]=0, [$1..N]); # Robert Israel, Mar 27 2019

Crossrefs

Sequence in context: A022139 A277351 A143707 * A003248 A353974 A071317

Adjacent sequences: A306986 A306987 A306988 * A306990 A306991 A306992

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2019

Status

approved