This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A122730 #5 Jun 13 2016 07:07:17
%S A122730 13,41,53,67,79,83,97,109,137,139,151,163,173,179,191,193,199,233,241,
%T A122730 263,271,277,313,317,331,347,359,373,383,389,397,421,433,439,443,449,
%U A122730 457,463,467,479,499,509,521,523,541,547,557,563,569,571,577,587,593
%N A122730 Primes that are the sum of 6 positive cubes.
%C A122730 By parity, there must be an odd number of odds in the sum. Hence this sequence is the union of primes which are the sum of an even and five odd cubes (such as x1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3); primes which are the sum of the cube of three even numbers and the cubes of three odd numbers (such as 53 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 3^3); and the primes which are the sum of the cube of an odd number and the cubes of five even numbers (such as 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 or 67 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3). A subset of this sequence is the primes which are the sum of the cubes of six distinct primes (i.e. of the form 2^3 + p^3 + q^3 + r^3 + s^3 + t^3 for p, q, r, s, t distinct odd primes) such as 8693 = 2^3 + 3^3 + 5^3 + 7^3 + 11^3 + 19^3. Another subsequence is the primes which are the sum of six cubes in two different ways, such as 313 = 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 = 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 6^3. Similarly, another subsequence is the primes which are the sum of six cubes in three different ways, such as 443. No prime can be the sum of two cubes (by factorization of the sum of two cubes).
%H A122730 Giovanni Resta, <a href="/A122730/b122730.txt">Table of n, a(n) for n = 1..10000</a>
%F A122730 A000040 INTERSECTION A003329.
%e A122730 a(1) = 13 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3.
%e A122730 a(2) = 41 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3
%e A122730 a(3) = 53 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 3^3.
%e A122730 a(4) = 67 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3.
%t A122730 up = 900; q = Range[up^(1/3)]^3; a = {0}; Do[ b = Select[ Union@ Flatten@ Table[e + a, {e, q}], # <= up &]; a = b, {k, 6}]; Select[a, PrimeQ] (* _Giovanni Resta_, Jun 13 2016 *)
%Y A122730 Cf. A000040, A003329.
%K A122730 easy,nonn
%O A122730 1,1
%A A122730 _Jonathan Vos Post_, Sep 23 2006
%E A122730 a(13)-a(53) from _Giovanni Resta_, Jun 13 2016