OFFSET
1,1
COMMENTS
Considering parity, a prime sum of three cubes cannot be the sum of three evens nor two odds and an even, but must be the sum of three odds (such as 1^3 + 3^3 + 9^3 = 757 or 3^3 + 5^3 + 9^3 = 881) or two evens and an odd (such as 1^3 + 2^3 + 10^3 = 1009). Without "distinct" we have solutions such as 1^3 + 1^3 + 3^3 = 29; 2^3 + 2^3 + 3^3 = 43; 1^3 + 1^3 + 5^3 = 127. A subset of the three odds subset is primes which are the sum of the cubes of three distinct primes, such as 3^3 + 5^3 + 11^3 = 1483; or 3^3 + 7^3 + 19^3 = 7229; or 7^3 + 11^3 + 23^3 = 13841; or 3^3 + 5^3 + 41^3 = 69073.
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
FORMULA
Primes in A024975.
EXAMPLE
a(1) = 73 = 1^3 + 2^3 + 4^3.
a(7) = 521 = 1^3 + 2^3 + 8^3.
MATHEMATICA
lst={}; Do[Do[Do[p=n^3+m^3+k^3; If[PrimeQ[p], AppendTo[lst, p]], {n, m+1, 4!}], {m, k+1, 4!}], {k, 4!}]; Take[Union[lst], 30] (* Vladimir Joseph Stephan Orlovsky, May 23 2009 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 23 2006
EXTENSIONS
Corrected and extended by Vladimir Joseph Stephan Orlovsky and T. D. Noe, Jul 16 2010
STATUS
approved