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 A130833 Sums of two or more distinct 4th powers of primes. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA {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}... EXAMPLE 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. MAPLE 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: sort(convert(S2, list)); # Robert Israel, Apr 27 2020 MATHEMATICA 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 *) CROSSREFS Cf. A000040, A000583, A030514, A192926, A193411. Sequence in context: A142765 A144130 A144131 * A130873 A193411 A094479 Adjacent sequences:  A130830 A130831 A130832 * A130834 A130835 A130836 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Jul 21 2011 STATUS approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)