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Sums of 3 but no fewer nonzero fourth powers.
5

%I #28 May 16 2021 01:49:59

%S 3,18,33,48,83,98,113,163,178,243,258,273,288,338,353,418,513,528,593,

%T 627,642,657,707,722,768,787,882,897,962,1137,1251,1266,1298,1313,

%U 1328,1331,1378,1393,1458,1506,1553,1568,1633,1808,1875,1922,1937,2002,2177

%N Sums of 3 but no fewer nonzero fourth powers.

%C Identical to A003337 for n = 1..87. - _Michael S. Branicky_, Mar 18 2021

%H Robert Israel, <a href="/A047714/b047714.txt">Table of n, a(n) for n = 1..10000</a>

%F A002377(a(n)) = 3. - _Robert Israel_, Jul 24 2020

%F Equals A003337 - A344187 - A000583. - _Sean A. Irvine_, May 15 2021

%p N:= 3000: # for terms <= N

%p F1:= {seq(i^4,i=1..floor(N^(1/4)))}: n1:= nops(F1):

%p F2:= select(`<=`,{seq(seq(F1[i]+F1[j],i=1..j),j=1..nops(F1))},N):

%p F3:= select(`<=`,{seq(seq(s+t,s=F1),t=F2)},N):

%p A:= sort(convert(F3 minus (F2 union F1), list)); # _Robert Israel_, Jul 24 2020

%o (Python)

%o def aupto(lim):

%o p1 = set(i**4 for i in range(1, int(lim**.25)+2) if i**4 <= lim)

%o p2 = set(a+b for a in p1 for b in p1 if a+b <= lim)

%o p3 = set(apb+c for apb in p2 for c in p1 if apb+c <= lim)

%o return sorted(p3-p2-p1)

%o print(aupto(2400)) # _Michael S. Branicky_, Mar 18 2021

%Y Cf. A000583, A002377, A336536, A344187.

%Y Subsequence of A003337.

%K nonn

%O 1,1

%A Arlin Anderson (starship1(AT)gmail.com)