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

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

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: A144130 A144131 A362321 * A130873 A193411 A094479

Adjacent sequences: A130830 A130831 A130832 * A130834 A130835 A130836

Keyword

nonn,easy

Author

Jonathan Vos Post, Jul 21 2011

Status

approved