A362248 a(n) is the number of locations 1..n-1 which can reach i=n-1, where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.

1, 1, 2, 3, 1, 5, 6, 7, 1, 1, 2, 11, 1, 13, 14, 15, 1, 1, 2, 3, 1, 5, 6, 23, 1, 1, 2, 27, 1, 29, 30, 31, 1, 1, 2, 3, 1, 5, 6, 7, 1, 1, 2, 11, 1, 13, 14, 47, 1, 1, 2, 3, 1, 5, 6, 55, 1, 1, 2, 59, 1, 61, 62, 63, 1, 1, 2, 3, 1, 5, 6, 7, 1, 1, 2, 11, 1, 13, 14, 15

Offset: 1

Author

Neal Gersh Tolunsky, May 12 2023

Keywords

• nonn

Comments

Note that location n-1 itself is counted as a term which can reach i=n-1.

Conjecture: a(n) is also the largest number such that starting point i=n can reach every previous location (with a(1)=1 and the same rule for jumps as in the current name).

A047619 appears to be the indices of 1's in this sequence.

A023758 appears to be the indices of terms for which a(n)=n-1.

A089633 appears to be the distinct values of the sequence (and its complement A158582 the missing values).

The sequence appears to consist of monotonically increasing runs of length 4.

It appears that a(A004767(n))=A100892(n) and a(A016825(n))=A100892(n)-1.

Examples

			a(6)=5 because there are 5 starting terms from which i=5 can be reached:
  1, 1, 2, 3, 1
  1->1->2---->1
We can see that i=1,2,3 and trivially 5 can reach i=5. i=4 can also reach i=5:
  1, 1, 2, 3, 1
  1<-------3
  1->1->2---->1
This is a total of 5 locations, so a(6)=5.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000
• Kevin Ryde, C Code

Crossrefs

Cf. A360746, A360745, A047619, A023758, A089633, A100892.

Programs

C

/* See links */

Extensions

a(24) onwards from Kevin Ryde, May 17 2023