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

1,1

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.

Links

Table of n, a(n) for n=1..65.

Example

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.

Crossrefs

Sequence in context: A047487 A327203 A048461 * A058590 A187711 A064627

Adjacent sequences: A338171 A338172 A338173 * A338175 A338176 A338177

Keyword

nonn

Author

Aidan Clarke, Nov 18 2020

Status

approved