A004842 Numbers that are the sum of at most 2 positive 5th powers.

0, 1, 2, 32, 33, 64, 243, 244, 275, 486, 1024, 1025, 1056, 1267, 2048, 3125, 3126, 3157, 3368, 4149, 6250, 7776, 7777, 7808, 8019, 8800, 10901, 15552, 16807, 16808, 16839, 17050, 17831, 19932, 24583, 32768, 32769, 32800, 33011, 33614, 33792, 35893, 40544

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 159 terms from Vincenzo Librandi)

Crossrefs

Cf. A004845.

Programs

Mathematica

Select[Table[n, {n, 0, 50000}], Length[PowersRepresentations[#, 2, 5]] > 0 &] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

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

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

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

Formula

a(n) << n^(5/2). - Charles R Greathouse IV, Nov 30 2014