1,1

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.

Primes in A024975. A000040 INTERSECTION {A024975 Sum of three distinct positive cubes}.

a(1) = 73 = 1^3 + 2^3 + 4^3.

a(7) = 1^3 + 2^3 + 8^3 = 521.

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] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 23 2009]

Cf. A000040, A024975.

Sequence in context: A142741 A088199 A140010 this_sequence A089786 A142894 A141909

Adjacent sequences: A122720 A122721 A122722 this_sequence A122724 A122725 A122726

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006