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

1,3

Comments

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

The sequence is nondecreasing.

Links

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

Example

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
                  ?

Crossrefs

Cf. A359807, A085262, A367026.

Sequence in context: A364843 A372678 A120456 * A115383 A219156 A210036

Adjacent sequences: A367036 A367037 A367038 * A367040 A367041 A367042

Keyword

nonn

Author

Neal Gersh Tolunsky, Nov 02 2023

Status

approved