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 A383858 #53 Jun 24 2025 16:18:53 %S A383858 2145,2310,10725,10374,101065,100050,255255,510510,1005993,1000350, %T A383858 1036035,1009470,10006081,10000130,10012065,10004610,100010225, %U A383858 100001300,100001195,100009910,111546435,223092870,1000083889,1000008758,1000001751,1000005270,1002569295,1001110110 %N A383858 Irregular triangle read by rows: T(n,k) (n >= 4, 4 <= k <= A384502(n)) is the smallest n-digit number m with k distinct prime factors, such that these factors can be divided into two subsets of at least two elements each, both summing to the same value. If no such number exists, T(n,k) = -1. %C A383858 The maximum values of k for each row n>=1 are respectively 0, 0, 0, 5, 5, 7, 7, ... %C A383858 The corresponding sums are: %C A383858 3+13 = 5+11, 3+11 = 2+5+7, 3+13 = 5+11, 3+19 = 2+7+13, 5+41 = 17+29, 2+29 = 3+5+23, 11+17 = 3+5+7+13, 5+7+17 = 2+3+11+13, 3+53 = 19+37, 2+19 = 3+5+13, 3+5+23 = 7+11+13, 5+7+23 = 2+3+11+19, 17+163 = 23+157, 2+383 = 5+7+373, 3+17+71 = 5+7+79, 2+7+71 = 3+5+11+61, 5+109 = 7+107, 2+383 = 5+7+373, 37+53 = 5+7+31+47, 5+11+103 = 2+7+13+97, 7+19+23 = 3+5+11+13+17, 3+5+19+23 = 2+7+11+13+17, ... %e A383858 T(4,4) = 2145 = 3*5*11*13 is the smallest four-digit number with four distinct prime factors (3, 5, 11, and 13), where the prime factors can be partitioned into two subsets of at least two elements each, both summing to the same value: 3+13 = 5+11. %e A383858 T(5,4) = 2310 = 2*3*5*7*11 is the smallest five-digit number with four distinct prime factors (2, 3, 5, 7 and 11), where the prime factors can be partitioned into two subsets of at least two elements each, both summing to the same value: 3+11 = 2+5+7. %e A383858 The lower triangle begins at T(4,4): %e A383858 [ 2145, 2310]; %e A383858 [ 10725, 10374]; %e A383858 [ 101065, 100050, 255255, 510510]; %e A383858 [ 1005993, 1000350, 1036035, 1009470]; %e A383858 [ 10006081, 10000130, 10012065, 10004610]; %e A383858 [100010225, 100001300, 100001195, 100009910, 111546435, 223092870]; ... %Y A383858 Cf. A001221, A365795, A382469, A383677, A383725, A383726, A383728, A383729, A384502. %K A383858 sign,base,tabf,more %O A383858 4,1 %A A383858 _Jean-Marc Rebert_, May 12 2025