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

1,2

Links

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

Example

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.

Crossrefs

Cf. A360746.

Sequence in context: A303540 A137266 A062948 * A358639 A358640 A096258

Adjacent sequences: A365156 A365157 A365158 * A365160 A365161 A365162

Keyword

nonn

Author

Neal Gersh Tolunsky, Aug 23 2023

Status

approved