A365576 a(1)=2; thereafter a(n) is the number of strongly connected components in the digraph of the sequence thus far, where jumps from location i to i+-a(i) are permitted (within 1..n-1).

2, 1, 2, 2, 3, 2, 2, 3, 3, 4, 5, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53

Offset: 1

Author

Neal Gersh Tolunsky, Sep 09 2023

Keywords

• nonn

Comments

If two locations j and k can reach other, then they belong to the same strongly connected component and can reach the same set of locations.

a(n) <= a(n-1) + 1.

Examples

			a(5)=3 because there are 3 distinct sets of locations which represent the indices reachable from a given location s.
Starting at s=1, we can visit the set of locations i = {1, 3}
  1  2  3  4
  2, 1, 2, 2
  2---->2
This is the same set of locations that can be visited from s=3. Since it is the same set, we only count it once:
  1  2  3  4
  2, 1, 2, 2
  2<----2
From s=2, we can visit the set of locations i = {1, 2, 3}:
  1  2  3  4
  2, 1, 2, 2
  2<-1->2
From s=4, we can visit another distinct set of locations i = {1, 2, 3, 4}
  1  2  3  4
  2, 1, 2, 2
     1<----2
  2<-1->2
This gives a total of 3 distinct sets of locations reachable from any starting index (equivalent to 3 strongly connected components):
  i = {1, 3}; i = {1, 2, 3}; and i = {1, 2, 3, 4}.
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A364882, A364392, A360744, A362248.