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A130833
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Sums of two or more distinct 4th powers of primes.
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2
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97, 641, 706, 722, 2417, 2482, 2498, 3026, 3042, 3107, 3123, 14657, 14722, 14738, 15266, 15282, 15347, 15363, 17042, 17058, 17123, 17139, 17667, 17683, 17748, 17764, 28577, 28642, 28658, 29186, 29202, 29267, 29283, 30962, 30978, 31043, 31059, 31587, 31603
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OFFSET
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1,1
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COMMENTS
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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).
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
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 97 = 2^4 + 3^4.
a(2) = 641 = 2^4 + 5^4.
a(3) = 706 = 3^4 + 5^4.
a(4) = 722 = 2^4 + 3^4 + 5^4.
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MAPLE
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N:= 40000: # for all terms <= N
S1:= {}:
S2:= {}:
p:= 1:
do
p:= nextprime(p);
if p^4 > N then break fi;
s:= p^4;
S2:= S2 union select(`<=`, map(`+`, S1 union S2, s), N);
S1:= S1 union {s};
od:
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MATHEMATICA
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nn=6; t = Sort@ Flatten@ Table[ n^4, {n, Prime@ Range@ nn}]; Select[Sort[
Plus @@@ Subsets[t, {2, nn}]], # < Prime[nn-1]^4 + Prime[nn]^4 &] (* Robert G. Wilson v, Jul 22 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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