A367039 a(1) = 0, a(2) = 1; thereafter a(n) is the largest index < n not equal to i +- a(i) for any i = 1..n-1.

0, 1, 2, 2, 4, 4, 4, 7, 8, 8, 8, 8, 12, 13, 14, 14, 16, 16, 16, 16, 16, 21, 22, 23, 24, 24, 26, 26, 28, 28, 28, 31, 32, 32, 32, 32, 32, 32, 38, 39, 40, 41, 42, 42, 44, 44, 46, 46, 48, 48, 48, 51, 52, 52, 52, 55, 56, 56, 56, 56, 60, 61, 62, 62, 64, 64, 64, 64, 64, 64, 64

Offset: 1

Author

Neal Gersh Tolunsky, Nov 02 2023

Keywords

• nonn

Comments

It appears that A085262 gives the distinct values of this sequence (except for the initial zero).

The sequence is nondecreasing.

Examples

			a(8)=7 because 7 is the largest index that cannot be expressed as the sum a(i)+-i for any i < n. 4 also cannot be expressed in this way, but it is smaller than 7.
Another way to see this is to consider each index i as a location from which one can jump a(i) terms forward or backward. For a(8)=7, we find the largest index which cannot be reached in this way (a smaller index being i=4):
0, 1, 2, 2, 4, 4, 4
0<-1
0, 1, 2, 2, 4, 4, 4
   1<----2
0, 1, 2, 2, 4, 4, 4
   1->2<----------4
0, 1, 2, 2, 4, 4, 4
         ?
0, 1, 2, 2, 4, 4, 4
      2---->4
0, 1, 2, 2, 4, 4, 4
         2---->4
0, 1, 2, 2, 4, 4, 4
                  ?
		

Links

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

Crossrefs

Cf. A359807, A085262, A367026.