cp's OEIS Frontend

A336536 Numbers n that can be written as both the sum of two nonzero fourth powers and the sum of three nonzero fourth powers.

%I A336536 #19 Mar 18 2021 17:46:43
%S A336536 4802,57122,76832,260642,388962,617057,913952,1229312,1847042,1957682,
%T A336536 3001250,3502322,3748322,3959297,4170272,4626882,6223392,6837602,
%U A336536 6959682,9872912,11529602,14623232,19668992,21112002,27691682,29552672,31322912,31505922,35701250,40127377,40302242,46712801,48020000,48355137
%N A336536 Numbers n that can be written as both the sum of two nonzero fourth powers and the sum of three nonzero fourth powers.
%C A336536 The fourth powers are not necessarily distinct.
%C A336536 If n is in the sequence, then so is k^4*n for every k.
%C A336536 The sum of two nonzero fourth powers is never a fourth power (a case of Fermat's last theorem).
%H A336536 Robert Israel, <a href="/A336536/b336536.txt">Table of n, a(n) for n = 1..1072</a>
%e A336536 a(3) = 76832 is in the sequence because 76832 = 14^4 + 14^4 = 6^4 + 10^4 + 16^4.
%e A336536 a(6) = 617057 is in the sequence because 617057 = 7^4 + 28^4 = 3^4 + 20^4 + 26^4.
%p A336536 N:= 10^8: # for terms <= N
%p A336536 F1:= {seq(i^4,i=1..floor(N^(1/4)))}: n1:= nops(F1):
%p A336536 F2:= select(`<=`,{seq(seq(F1[i]+F1[j],i=1..j),j=1..nops(F1))},N):
%p A336536 F3:= select(`<=`,{seq(seq(s+t,s=F1),t=F2)},N):
%p A336536 sort(convert(F3 intersect F2,list));
%o A336536 (Python)
%o A336536 def aupto(lim):
%o A336536   p1 = set(i**4 for i in range(1, int(lim**.25)+2) if i**4 <= lim)
%o A336536   p2 = set(a+b for a in p1 for b in p1 if a+b <= lim)
%o A336536   p3 = set(apb+c for apb in p2 for c in p1 if apb+c <= lim)
%o A336536   return sorted(p3 & p2)
%o A336536 print(aupto(5*10**7)) # _Michael S. Branicky_, Mar 18 2021
%Y A336536 Cf. A000583, A003294, A047714.
%Y A336536 Intersection of A003336 and A003337.
%K A336536 nonn
%O A336536 1,1
%A A336536 _Robert Israel_, Jul 24 2020