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%I #26 Oct 29 2023 21:50:16
%S 0,1,2,32,33,64,243,244,275,486,1024,1025,1056,1267,2048,3125,3126,
%T 3157,3368,4149,6250,7776,7777,7808,8019,8800,10901,15552,16807,16808,
%U 16839,17050,17831,19932,24583,32768,32769,32800,33011,33614,33792,35893,40544
%N Numbers that are the sum of at most 2 positive 5th powers.
%H Charles R Greathouse IV, <a href="/A004842/b004842.txt">Table of n, a(n) for n = 1..10000</a> (first 159 terms from Vincenzo Librandi)
%F a(n) << n^(5/2). - _Charles R Greathouse IV_, Nov 30 2014
%t Select[Table[n, {n, 0, 50000}], Length[PowersRepresentations[#, 2, 5]] > 0 &] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%o (PARI) T=thueinit('z^5+1);is(n)=n==0 || #select(v->min(v[1],v[2])>=0, thue(T, n))>0 \\ _Charles R Greathouse IV_, Nov 30 2014
%o (PARI) is(n)=for(m=sqrtnint(n\2,5), sqrtnint(n,5), if(ispower(n-m^5,5), return(1))); 0 \\ _Charles R Greathouse IV_, Nov 30 2014
%o (PARI) list(lim)=my(v=List(),n5); for(n=0,sqrtnint(lim\=1,5), n5=n^5; for(m=0, min(sqrtnint(lim-n5,5),n), listput(v, n5+m^5))); Set(v) \\ _Charles R Greathouse IV_, Nov 30 2014
%Y Cf. A004845.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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