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A130833 Sums of two or more distinct 4th powers of primes.

%I A130833 #24 Apr 27 2020 17:34:53
%S A130833 97,641,706,722,2417,2482,2498,3026,3042,3107,3123,14657,14722,14738,
%T A130833 15266,15282,15347,15363,17042,17058,17123,17139,17667,17683,17748,
%U A130833 17764,28577,28642,28658,29186,29202,29267,29283,30962,30978,31043,31059,31587,31603
%N A130833 Sums of two or more distinct 4th powers of primes.
%C A130833 This is to cubes and A030078 as A192926 is to 4th powers and A030514. The subsequence of primes which are sums of two or more distinct 4th powers of primes begins 97, 641, 2417 (A193411).
%C A130833 The first term that arises in more than one way is 6539044 = 11^4 + 23^4 + 41^4 + 43^4 = 13^4 + 29^4 + 31^4 + 47^4. - _Robert Israel_, Apr 27 2020
%H A130833 Robert Israel, <a href="/A130833/b130833.txt">Table of n, a(n) for n = 1..10000</a>
%F A130833 {A030078(i) + A030078(j) for i not equal to j} UNION {A030078(i) + A030078(j) + A030078(k) for i not equal to j not equal to k} UNION {A030078(i) + A030078(j) + A030078(k) + A030078(L) for i not equal to j not equal to k not equal to L}...
%e A130833 a(1) = 97 = 2^4 + 3^4.
%e A130833 a(2) = 641 = 2^4 + 5^4.
%e A130833 a(3) = 706 = 3^4 + 5^4.
%e A130833 a(4) = 722 = 2^4 + 3^4 + 5^4.
%p A130833 N:= 40000: # for all terms <= N
%p A130833 S1:= {}:
%p A130833 S2:= {}:
%p A130833 p:= 1:
%p A130833 do
%p A130833   p:= nextprime(p);
%p A130833   if p^4 > N then break fi;
%p A130833   s:= p^4;
%p A130833   S2:= S2 union select(`<=`,map(`+`,S1 union S2, s), N);
%p A130833   S1:= S1 union {s};
%p A130833 od:
%p A130833 sort(convert(S2,list)); # _Robert Israel_, Apr 27 2020
%t A130833 nn=6; t = Sort@ Flatten@ Table[ n^4, {n, Prime@ Range@ nn}]; Select[Sort[
%t A130833 Plus @@@ Subsets[t, {2, nn}]], # < Prime[nn-1]^4 + Prime[nn]^4 &] (* _Robert G. Wilson v_, Jul 22 2011 *)
%Y A130833 Cf. A000040, A000583, A030514, A192926, A193411.
%K A130833 nonn,easy
%O A130833 1,1
%A A130833 _Jonathan Vos Post_, Jul 21 2011