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Numbers of the form 5^(2*i+1)*(5*j+-2).
1

%I #24 Apr 16 2015 17:02:32

%S 10,15,35,40,60,65,85,90,110,115,135,140,160,165,185,190,210,215,235,

%T 240,250,260,265,285,290,310,315,335,340,360,365,375,385,390,410,415,

%U 435,440,460,465,485,490,510,515,535,540,560,565,585,590

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

%C The numbers not of the form x^2+2y^2+5z^2.

%H David A. Corneth, <a href="/A055049/b055049.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).

%F a(n) ~ 12 * n. - _David A. Corneth_, Apr 12 2015

%e a(19) = a(1) + 25 * floor((19 - 1)/2) = 235 - _David A. Corneth_, Mar 31 2015

%p N:= 1000: # to get all terms <= N

%p A:= {}:

%p for i from 0 to floor((log[5](N)-1)/2) do

%p a:= 5^(2*i+1);

%p A:= A union {seq(a*(5*j+2),j=0..floor((N/a-2)/5))}

%p union {seq(a*(5*j-2),j=1..floor((N/a+2)/5))};

%p od:

%p A; # if using Maple 11 or earlier, uncomment the next line

%p # sort(convert(A,list)); # _Robert Israel_, Apr 13 2015

%t Take[ Union@ Flatten@ Table[ 5^(2i + 1) (j), {i, 0, 1}, {j, Select[ Range@ 120, Mod[#, 5] == 2 || Mod[#, 5] == 3 &] }], 50] (* _Robert G. Wilson v_, Mar 30 2015 *)

%o (PARI) is(n) = v=valuation(n,5);r=(n/5^v)%5;v%2==1&&(r==2||r==3) \\ _David A. Corneth_, Apr 12 2015

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jun 02 2000