A123597 Primes of the form p^3 + q^3 + r^3, where p, q and r are primes.

43, 179, 277, 359, 397, 593, 811, 1483, 2017, 2213, 2251, 2447, 2689, 4421, 4519, 4967, 5381, 6271, 7109, 7229, 9181, 9521, 10169, 11897, 12853, 13103, 13841, 14489, 16561, 17107, 20357, 24443, 24677, 25747, 26711, 27917, 30161, 30259, 31193, 31247, 32579, 36161

Offset

1,1

Comments

a(n) is a subset of A007490(n) = {3, 17, 29, 43, 73, 127, 179, 197, 251, 277, ...}, i.e., primes of the form x^3 + y^3 + z^3.

Links

Table of n, a(n) for n=1..42.

Example

a(1) = 43 because 43 = 2^3 + 2^3 + 3^3 is prime and 2^3 + 2^3 + 2^3 = 24 is composite.

Mathematica

lst={}; Do[Do[Do[p=n^3+m^3+k^3; If[PrimeQ[p]&&PrimeQ[n]&&PrimeQ[m]&&PrimeQ[k], AppendTo[lst, p]], {n, 4!}], {m, 4!}], {k, 4!}]; Take[Union[lst], 16] (* Vladimir Joseph Stephan Orlovsky, May 23 2009 *)
With[{nn=40}, Select[Total/@Tuples[Prime[Range[nn]]^3, 3], PrimeQ[#]&&#<= nn^3+ 16&]]//Union (* Harvey P. Dale, Sep 08 2021 *)

Crossrefs

Cf. A007490 = Primes of form x^3 + y^3 + z^3.

Sequence in context: A162295 A187722 A158628 * A138631 A309905 A142115

Adjacent sequences: A123594 A123595 A123596 * A123598 A123599 A123600

Keyword

nonn

Author

Alexander Adamchuk, Nov 14 2006

Status

approved