A122723 Primes that are the sum of three distinct positive cubes.

73, 197, 251, 281, 307, 349, 521, 547, 577, 701, 757, 853, 863, 881, 919, 953, 1009, 1091, 1217, 1249, 1483, 1559, 1637, 1861, 1907, 2069, 2087, 2267, 2269, 2287, 2339, 2477, 2521, 2729, 2753, 2843, 2927, 2953, 2969, 3067, 3257, 3413, 3457, 3527, 3529

Offset: 1

Author

Jonathan Vos Post, Sep 23 2006

Keywords

• easy
• nonn

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.

Examples

			a(1) = 73 = 1^3 + 2^3 + 4^3.
a(7) = 521 = 1^3 + 2^3 + 8^3.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A000040, A024975.

Programs

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 *)

Formula

Primes in A024975.

Extensions

Corrected and extended by Vladimir Joseph Stephan Orlovsky and T. D. Noe, Jul 16 2010