

A122723


Primes that are the sum of three distinct positive cubes.


7



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



