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%I #39 Jul 09 2022 11:06:55
%S 5,13,20,21,29,37,45,52,53,61,69,77,80,84,85,93,101,109,116,117,125,
%T 133,141,148,149,157,165,173,180,181,189,197,205,208,212,213,221,229,
%U 237,244,245,253,261,269,276,277,285,293,301,308,309,317
%N Numbers of the form 4^i*(8*j+5).
%C Numbers not of the form x^2+2y^2+6z^2.
%H Reinhard Zumkeller, <a href="/A055045/b055045.txt">Table of n, a(n) for n = 1..10000</a>
%H L. E. Dickson, <a href="http://dx.doi.org/10.1090/S0002-9904-1927-04312-9">Integers represented by positive ternary quadratic forms</a>, Bull. Amer. Math. Soc. 33 (1927), 63-70. See Theorem XI.
%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).
%F a(n) = 6n + O(log n). - _Charles R Greathouse IV_, Dec 19 2013
%o (PARI) is(n)=n/=4^valuation(n,4); n%8==5 \\ _Charles R Greathouse IV_ and _V. Raman_, Dec 19 2013
%o (Haskell)
%o a055045 n = a055045_list !! (n-1)
%o a055045_list = filter ((== 5) . (flip mod 8) . f) [1..] where
%o f x = if r == 0 then f x' else x where (x', r) = divMod x 4
%o -- _Reinhard Zumkeller_, Jan 02 2014
%o (Python)
%o from itertools import count, islice
%o def A055045_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda n:not (m:=(~n&n-1).bit_length())&1 and (n>>m)&7==5, count(max(startvalue, 1)))
%o A055045_list = list(islice(A055045_gen(), 30)) # _Chai Wah Wu_, Jul 09 2022
%Y Cf. A004215, A055046, A234000.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Jun 01 2000
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