A055042 - OEIS

%I #14 Apr 19 2021 10:29:54

%S 10,26,40,42,58,74,90,104,106,122,138,154,160,168,170,186,202,218,232,

%T 234,250,266,282,296,298,314,330,346,360,362,378,394,410,416,424,426,

%U 442,458,474,488,490,506,522,538,552,554,570,586,602,616

%N Numbers of the form 2^(2i+1)*(8*j+5).

%C These are also the numbers not of the form x^2+2y^2+3z^2.

%D B. W. Jones, The Arithmetic of Quadratic Forms, Carus Monograph 10, Math. Assoc. America, 1967; Problem 60, p. 204.

%H David A. Corneth, <a href="/A055042/b055042.txt">Table of n, a(n) for n = 1..10000</a>

%H L. J. Mordell, <a href="http://dx.doi.org/10.1093/qmath/os-1.1.276">A new Waring's problem with squares of linear forms</a>, Quart. J. Math., 1 (1930), 276-288 (see p. 283).

%e 42 = 21*2 = 2^(2*0 + 1)*(8*2 + 5) is in the sequence. - _David A. Corneth_, Apr 18 2021

%o (PARI) upto(n) = { my(res = List()); for(i = 0, logint(n\2, 2), forstep(j = 5, n>>(2*i+1), 8, listput(res, 4^i*2*j) ) ); Set(res) } \\ _David A. Corneth_, Apr 18 2021

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Jun 01 2000