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A306469 Numbers not of the form x^2+2*y^2+2*y*z+4*z^2 (with x, y, z all >= 0). 2
7, 10, 14, 15, 21, 30, 35, 39, 42, 63, 70, 79, 84, 91, 94, 119, 126, 130, 133, 140, 168, 175, 182, 189, 210, 217, 231, 238, 259, 266, 280, 287, 315, 329, 336, 343, 359, 364, 378, 382, 385, 391, 399, 413, 427, 434, 462, 476, 483, 490, 511, 525, 532, 546, 560 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It appears that the only terms not divisible by 7 are 10, 15, 30, 39, 79, 94, 130, 359, 382, 391, 754, and 1546. - Robert Israel, Mar 27 2019
LINKS
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 while x^2<=N do
for y from 0 while x^2 + 2*y^2 <= N do
for z from 0 do
v:= x^2 + 2*y^2 + 2*y*z + 4*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
Cf. A097634 (without the nonnegative requirement).
Sequence in context: A123834 A064629 A215579 * A059752 A080205 A108980
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 26 2019
EXTENSIONS
Thanks to Robert Israel for pointing out that I neglected to mention x, y, z >= 0. - N. J. A. Sloane, Mar 27 2019
STATUS
approved

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Last modified April 17 18:43 EDT 2024. Contains 371765 sequences. (Running on oeis4.)