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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

%I #44 Mar 28 2019 00:47:17

%S 7,10,14,15,21,30,35,39,42,63,70,79,84,91,94,119,126,130,133,140,168,

%T 175,182,189,210,217,231,238,259,266,280,287,315,329,336,343,359,364,

%U 378,382,385,391,399,413,427,434,462,476,483,490,511,525,532,546,560

%N Numbers not of the form x^2+2*y^2+2*y*z+4*z^2 (with x, y, z all >= 0).

%C 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

%H Robert Israel, <a href="/A306469/b306469.txt">Table of n, a(n) for n = 1..10000</a>

%H Irving Kaplansky, <a href="https://doi.org/10.1090/S0025-5718-1995-1265017-2">The first nontrivial genus of positive definite ternary forms</a>, Mathematics of Computation, Vol. 64 (1995): 341-345.

%p N:= 1000: # for terms <= N

%p V:= Array(0..N):

%p for x from 0 while x^2<=N do

%p for y from 0 while x^2 + 2*y^2 <= N do

%p for z from 0 do

%p v:= x^2 + 2*y^2 + 2*y*z + 4*z^2;

%p if v > N then break fi;

%p V[v]:= 1;

%p od od od:

%p select(t -> V[t]=0, [$1..N]); # _Robert Israel_, Mar 27 2019

%Y Cf. A097634 (without the nonnegative requirement).

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Mar 26 2019

%E Thanks to _Robert Israel_ for pointing out that I neglected to mention x, y, z >= 0. - _N. J. A. Sloane_, Mar 27 2019

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Last modified May 22 10:24 EDT 2024. Contains 372745 sequences. (Running on oeis4.)