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

1,1

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

Cf. A000040, A024975.

Sequence in context: A142741 A088199 A140010 * A089786 A142894 A141909

Adjacent sequences: A122720 A122721 A122722 * A122724 A122725 A122726

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