A157026 Primes p with the property that p^3=n^3+m^3+k^3.

19, 29, 41, 53, 67, 71, 89, 97, 103, 113, 127, 137, 139, 151, 167, 179, 181, 191, 193, 197, 199, 229, 239, 241, 251, 269, 281, 293, 307, 311, 317, 331, 349, 373, 379, 383, 389, 419, 431, 461, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541

Offset

1,1

Comments

19^3=18^3+10^3+3^3, 29^3=27^3+15^3+11^3, 41^3=33^3+32^3+6^3, ... Prime number power 3 = sum of 3 cubes.

Links

Table of n, a(n) for n=1..50.

Mathematica

q=3; lst={}; Do[Do[Do[p=n^q+m^q+k^q; p=p^(1/q); If[PrimeQ[p], AppendTo[lst, p]], {n, m+1, 6!}], {m, k+1, 3*5!}], {k, 5!}]; Length[lst]; Length[Union[lst]]; Take[Union[lst], 20]
Select[Prime[Range[100]], Length[PowersRepresentations[#^3, 3, 3]]>1&] (* Harvey P. Dale, Nov 22 2014 *)

Crossrefs

Sequence in context: A109276 A133765 A158846 * A240724 A274849 A276049

Adjacent sequences: A157023 A157024 A157025 * A157027 A157028 A157029

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 21 2009

Extensions

More terms from Harvey P. Dale, Nov 22 2014

Status

approved