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 A224534 #34 May 07 2025 13:45:51
%S A224534 19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,
%T A224534 109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
%U A224534 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307
%N A224534 Prime numbers that are the sum of three distinct prime numbers.
%C A224534 Similar to Goldbach's weak conjecture.
%C A224534 Primes in A124867, and by the comment in A124867 also the set of all primes >=19. - _R. J. Mathar_, Apr 19 2013
%C A224534 "Goldbach's original conjecture (sometimes called the 'ternary' Goldbach conjecture), written in a June 7, 1742 letter to Euler, states 'at least it seems that every number that is greater than 2 is the sum of three primes' (Goldbach 1742; Dickson 2005, p. 421). Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed." [Weisstein] - _Jonathan Vos Post_, May 15 2013
%H A224534 H. A. Helfgott and David J. Platt, <a href="http://arxiv.org/abs/1305.3062">Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30</a>, arXiv:1305.3062 [math.NT], 2013-2014.
%H A224534 H. A. Helfgott and David J. Platt, <a href="http://dx.doi.org/10.1080/10586458.2013.831742">Numerical verification of the Ternary Goldbach Conjecture up to 8.875*10^30</a>, Exp. Math. 22 (4) (2013) 406-409.
%H A224534 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach conjecture</a>
%H A224534 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach's_conjecture">Goldbach's conjecture</a>
%H A224534 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach's_weak_conjecture">Goldbach's weak conjecture</a>
%e A224534 19 = 3 + 5 + 11.
%t A224534 Union[Select[Total /@ Subsets[Prime[Range[2, 30]], {3}], PrimeQ]]
%Y A224534 Cf. A002372, A002375, A024684 (number of sums), A224535, A166063, A166061, A071621.
%K A224534 nonn
%O A224534 1,1
%A A224534 _T. D. Noe_, Apr 15 2013