A126704 Prime numbers that are the sum of three distinct positive sixth powers.

4889, 50753, 51481, 66377, 262937, 308801, 797681, 840241, 1000793, 1046657, 1772291, 2303003, 2986777, 3032641, 3107729, 3365777, 4757609, 4804201, 5135609, 7530329, 7534361, 8061041, 8065073, 10516249, 12394721, 14638753

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

4889 = 2^6 + 3^6 + 4^6 = 64 + 729 + 4096.
66377 = 4^6 + 5^6 + 6^6 = 4096 + 15625 + 46656.

Maple

N:= 10^10; # to find all terms <= N
A := {}:
for a from 1 to iroot(N, 6) do
  for b from 1 to a-1 while a^6 + b^6 < N do
    for c from (a+b) mod 2 + 1 to b-1 by 2 do
      r:= a^6 + b^6 + c^6;
      if r > N then break fi;
      if isprime(r) then A:= A union {r} fi;
od od od:
sort(convert(A, list)); # Robert Israel, Dec 15 2015

Mathematica

Union[Select[Total/@Subsets[Range[20]^6, {3}], PrimeQ]] (* Harvey P. Dale, Apr 20 2013 *)

Prog

(PARI) {m=16; p=m^6; w=[]; for(i=1, m-2, for(j=i+1, m-1, for(k=j+1, m, if((n=i^6+j^6+k^6)<p&&isprime(n), w=concat(w, n))))); w=vecsort(w); for(h=1, #w, print1(w[h], ", "))} /* Klaus Brockhaus, Feb 16 2007 */

Crossrefs

Cf. A125516, A126657, A126658.

Sequence in context: A075294 A206273 A086127 * A251325 A186478 A220059

Adjacent sequences: A126701 A126702 A126703 * A126705 A126706 A126707

Keyword

nonn

Author

Tomas Xordan, Feb 11 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 16 2007

Status

approved