cp's OEIS Frontend

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.

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.

Original entry on oeis.org

2145, 2310, 10725, 10374, 101065, 100050, 255255, 510510, 1005993, 1000350, 1036035, 1009470, 10006081, 10000130, 10012065, 10004610, 100010225, 100001300, 100001195, 100009910, 111546435, 223092870, 1000083889, 1000008758, 1000001751, 1000005270, 1002569295, 1001110110
Offset: 4

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Author

Jean-Marc Rebert, May 12 2025

Keywords

Comments

The maximum values of k for each row n>=1 are respectively 0, 0, 0, 5, 5, 7, 7, ...
The corresponding sums are:
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, ...

Examples

			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.
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.
The lower triangle begins at T(4,4):
[     2145,      2310];
[    10725,     10374];
[   101065,    100050,    255255,    510510];
[  1005993,   1000350,   1036035,   1009470];
[ 10006081,  10000130,  10012065,  10004610];
[100010225, 100001300, 100001195, 100009910, 111546435, 223092870]; ...
		

Crossrefs