A365159 a(n)=n for n<=3, and thereafter, a(n) is the number of locations 1..n-1 which cannot be reached starting from i=n-1, where jumps from location i to i +- a(i) are permitted (within 1..n-1). See example.

1, 2, 3, 2, 2, 3, 4, 4, 3, 6, 4, 6, 8, 5, 9, 10, 11, 12, 13, 13, 11, 11, 13, 13, 15, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 26, 26, 18, 26, 29, 20, 23, 24, 25, 26, 27, 28, 29, 29, 28, 31, 29, 28, 29, 30, 31, 32, 33, 34, 34, 38, 27, 39, 40, 41, 42, 42

Offset: 1

Author

Neal Gersh Tolunsky, Aug 23 2023

Keywords

• nonn

Examples

			a(9)=3 because there are 3 locations that cannot be reached starting from i=n-1=8, where a(8)=4. We start by finding the locations that can be reached (each line shows the next unvisited location(s) we can reach from the term(s) in the previous iteration):
1, 2, 3, 2, 2, 3, 4, 4
         2<----------4
1, 2, 3, 2, 2, 3, 4, 4
   2<----2---->3
1, 2, 3, 2, 2, 3, 4, 4
      3<-------3
We visited 5 locations (i = 2, 3, 4, 6, and 8) and can visit no more:
1, 2, 3, 2, 2, 3, 4, 4
   2  3  2     3     4
This leaves a total of 3 locations that could not be reached (i = 1, 5, and 7) from i=8, so a(9)=3.
		

Links

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

Crossrefs

Cf. A360746.