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 A317678 #15 Sep 01 2018 02:03:15
%S A317678 1,11,17,37,43,61,29,31,37,41,67,71,73,83,101,97,101,103,107,113,139,
%T A317678 179,181,191,199,211,223,241,223,227,229,233,239,257,269,283,223,227,
%U A317678 229,233,239,241,251,257,317,347,349,353,359,367,373,397,401,421,443
%N A317678 Sets of n distinct primes p_i in ascending order, written as triangle, such that S_n = Sum_{k=1..n} p_k is minimized and that there exists a compensation set of n primes q_j with q_j = n*p_j - Sum_{k=1..n,k!=j} p_k, j=1..n such that the set union {p_j} U {q_j} contains 2*n distinct primes and Sum_{k=1..n} q_k = S_n.
%C A317678 In case of ties, i.e., if more than one set exists for the same minimal sum S_n, the lexicographically least set is chosen. Since the condition of distinctness of {p_j} U {q_j} cannot be satisfied for n=1, the sets p = q = {1} are assumed to complete the triangle.
%C A317678 The minimal sums S_n are provided in A317680 and the corresponding compensation sets are provided in A317679. The compensation set is a solution to the "fair compensation" problem. n persons who own individual shares of p_i units of an asset agree to equally share those assets among themselves and a person n+1, who owns 0 units of this asset, but is willing to pay S_n units of compensation, e.g. money, to buy his share of S_n/(n+1) units of the asset. S_n/(n+1) doesn't need to be integer. q_j as defined above is a fair compensation for person j's relinquishment of assets by equipartitioning, assuming a constant price per asset.
%H A317678 IBM Research, <a href="https://www.research.ibm.com/haifa/ponderthis/challenges/August2018.html">Ponder This August 2018 - Challenge</a>, 9th row of table is one of many solutions.
%e A317678 Table begins:
%e A317678 n Sum p_k q_k
%e A317678 A317680 A317679
%e A317678 1 1 1 1
%e A317678 2 28 11 17 5 23
%e A317678 3 141 37 43 61 7 31 103
%e A317678 4 138 29 31 37 41 7 17 47 67
%e A317678 5 395 67 71 73 83 101 7 31 43 103 211
%e A317678 6 660 97 101 103 107 113 139 19 47 61 89 131 313
%Y A317678 Cf. A024939, A317679, A317680.
%K A317678 nonn,tabl
%O A317678 1,2
%A A317678 _Hugo Pfoertner_, Aug 10 2018