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 A122728 #15 Aug 31 2025 18:04:39
%S A122728 11,37,67,89,107,137,149,163,191,193,233,271,317,353,367,379,383,409,
%T A122728 439,461,467,479,503,523,541,587,593,601,613,631,641,653,691,709,739,
%U A122728 751,773,809,821,839,857,863,883,887,919,929,947,971,983,991,1033,1069
%N A122728 Primes that are the sum of 4 positive cubes.
%C A122728 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 the cube of an even number and the cubes of three odd numbers (such as 11 = 1^3 + 1^3 + 1^3 + 2^3) and the primes which are the sum of the cube of an odd number and the cubes of three even numbers (such as 149 = 2^3 + 2^3 + 2^3 + 5^3). A subset of this sequence is the primes which are the sum of the cubes of four distinct primes (i.e. of the form 2^3 + p^3 + q^3 + r^3 for p, q, r, distinct odd primes) such as 503 = 2^3 + 3^3 + 5^3 + 7^3; or 2357 = 2^3 + 3^3 + 5^3 + 13^3. No prime can be the sum of two cubes (by factorization of the sum of two cubes).
%H A122728 Giovanni Resta, <a href="/A122728/b122728.txt">Table of n, a(n) for n = 1..10000</a>
%F A122728 A000040 INTERSECTION A003327.
%e A122728 a(1) = 11 = 1^3 + 1^3 + 1^3 + 2^3.
%e A122728 a(2) = 37 = 1^3 + 1^3 + 2^3 + 3^3.
%e A122728 a(3) = 67 = 1^3 + 1^3 + 1^3 + 4^3.
%t A122728 mx = 1000; lim = Floor[(mx - 3)^(1/3)]; Select[Union[Total /@ Tuples[Range[lim]^3, {4}]], # <= mx && PrimeQ[#] &] (* _Harvey P. Dale_, May 25 2011 *)
%Y A122728 Cf. A000040, A003327.
%K A122728 easy,nonn,changed
%O A122728 1,1
%A A122728 _Jonathan Vos Post_, Sep 23 2006
%E A122728 More terms from _Harvey P. Dale_, May 25 2011