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

1,3

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A004845.

Sequence in context: A357176 A018802 A166487 * A022378 A306950 A193419

Adjacent sequences: A004839 A004840 A004841 * A004843 A004844 A004845

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved