A147857 Differences of two positive 4th powers.

0, 15, 65, 80, 175, 240, 255, 369, 544, 609, 624, 671, 1040, 1105, 1215, 1280, 1295, 1695, 1776, 2145, 2320, 2385, 2400, 2465, 2800, 3439, 3471, 3840, 4015, 4080, 4095, 4160, 4641, 5265, 5904, 5936, 6095, 6305, 6480, 6545, 6560, 7599, 7825, 8080, 8704

Offset: 1

Author

Max Alekseyev, Nov 15 2008, Nov 19 2008

Keywords

• nonn

Comments

If n belongs to this sequence then so does n*m^4 for any positive integer m. Primitive elements (i.e., not of the form n*m^4 for m>1) are listed in A147858.

There is no square in this sequence except 0. - Altug Alkan, Apr 08 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A152044.

Cf. A147854, A147856, A147858

Programs

Maple

N:= 10^4: # to get all terms <= N
Res:= {0}:
for a from 1 to floor(sqrt(N-2)) do
  if a^4 > N then bmin:= ceil((a^4-N)^(1/4)) else bmin:= 1 fi;
  Res:= Res union {seq(a^4-b^4, b=bmin..a-1)}
od:
sort(convert(Res,list)); # Robert Israel, Sep 28 2018

Mathematica

nn = 50; Take[Union @@ Map[Differences, Union@ Map[Sort@ # &, Tuples[Range[Ceiling[nn/3]], {2}]]^4], nn] (* Michael De Vlieger, Apr 09 2016 *)

Extensions

Offset changed by Robert Israel, Sep 28 2018