cp's OEIS Frontend

A360382 Least integer m whose n-th power can be written as a sum of four distinct positive n-th powers.

%I A360382 #22 Mar 04 2023 15:27:54
%S A360382 10,9,13,353,144
%N A360382 Least integer m whose n-th power can be written as a sum of four distinct positive n-th powers.
%F A360382 a(n) = Minimum(m) such that m^n = a^n + b^n + c^n + d^n and 0 < a < b < c < d < m.
%e A360382 a(3) = 13 because 13^3 = 1^3 + 5^3 + 7^3 + 12^3 and no smaller cube may be written as the sum of 4 positive distinct cubes.
%e A360382 Terms in this sequence and their representations are:
%e A360382   10^1 = 1 + 2 + 3 + 4.
%e A360382   9^2 = 2^2 + 4^2 + 5^2 + 6^2.
%e A360382   13^3 = 1^3 + 5^3 + 7^3 + 12^3.
%e A360382   353^4 = 30^4 + 120^4 + 272^4 + 315^4.
%e A360382   144^5 = 27^5 + 84^5 + 110^5 + 133^5.
%t A360382 n = 5; SelectFirst[
%t A360382  Range[200], (s =
%t A360382     IntegerPartitions[#^n, {4, 4}, Range[1, # - 1]^n]^(1/n); (Select[
%t A360382       s, #[[1]] > #[[2]] > #[[3]] > #[[4]] > 0 &] != {})) &]
%o A360382 (Python)
%o A360382 def s(n):
%o A360382     p=[k**n for k in range(360)]
%o A360382     for k in range(4,360):
%o A360382         for d in range(k-1,3,-1):
%o A360382             if 4*p[d]>p[k]:
%o A360382                 cc=p[k]-p[d]
%o A360382                 for c in range(d-1,2,-1):
%o A360382                     if 3*p[c]>cc:
%o A360382                         bb=cc-p[c]
%o A360382                         for b in range(c-1,1,-1):
%o A360382                            if 2*p[b]>bb:
%o A360382                                aa=bb-p[b]
%o A360382                                if aa>0 and aa in p:
%o A360382                                    a=round(aa**(1/n))
%o A360382                                    return(n,k,[a,b,c,d])
%o A360382 for n in range(1,6):
%o A360382     print(s(n))
%Y A360382 Cf. A007666, A039664, A003294, A134341.
%K A360382 nonn,more
%O A360382 1,1
%A A360382 _Zhining Yang_, Feb 04 2023