A338174 The largest value that integer n is connected to in a web where every integer n has n connections, each integer is connected to the lowest values possible, and new values are added in phases.

2, 3, 5, 7, 10, 11, 13, 16, 20, 25, 21, 22, 23, 24, 25, 26, 28, 31, 35, 40, 46, 54, 64, 76, 90, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 96, 102, 110, 120, 132, 146

Offset: 1

Author

Aidan Clarke, Nov 18 2020

Keywords

• nonn

Comments

The concept of this sequence is based on a web where every possible connection in the web is made with the numbers written so far, and then new numbers are added for every connection that needs to be made.

Examples

			Start with a map of nothing but 1.
   1 has 0 connections.
So we add 2 and connect it.
   1 has 1 connection (2)
   2 has 1 connection (1)
Now we need one more number to connect with 2, so we add 3.
   2 has 2 connections (1,3)
   3 has 1 connection (2)
Now because 3 needs two more numbers, we add 4 and 5 at once, and make as many connections as possible.
   3 has 3 connections (2,4,5)
   4 has 2 connections (3,5)
   5 has 2 connections (3,4)
We need five more numbers because 4 lacks two connections, and 5 lacks three connections, so we add 6,7,8,9,10.
   4 has 4 connections (3,5,6,7)
   5 has 5 connections (3,4,8,9,10)
   6 has 5 connections (4,7,8,9,10)
   7 has 5 connections (4,6,8,9,10)
   8 has 5 connections (5,6,7,9,10)
   9 has 5 connections (5,6,7,8,10)
   10 has 5 connections (5,6,7,8,9)
This continues indefinitely.