A367026 a(1) = 0, a(2) = 1; thereafter a(n) is the smallest index < n not equal to i +- a(i) for any i = 1..n-1.

0, 1, 2, 2, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 8, 8, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 25, 25, 25, 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40

Offset: 1

Author

Neal Gersh Tolunsky, Nov 01 2023

Keywords

• nonn

Comments

The sequence is nondecreasing.

Examples

			a(3)=2 because a(2)=1 has i - a(i) = 2-1 = 1, which means that 1 cannot be a term (since it can be expressed as i - a(i) for some index i in the sequence thus far). 2 cannot be reached in this way, so a(3)=2.
a(5)=4 because 1 = 2 - a(2) (as seen above); 2 = 4 - a(4); and 3 = 2 + a(2). 4 cannot be the answer to any such expression, so a(5)=4.
Another way to see this is to consider each index i as a location from which one can jump forward or back a(i) terms. To find a(5), we see that there is no way to reach i=4, which is the smallest-indexed location with this property.
0, 1, 2, 2
0<-1
0, 1, 2, 2
   1<----2
0, 1, 2, 2
   1->2
0, 1, 2, 2
         ?
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
• Neal Gersh Tolunsky, Graph of first 16674 run lengths

Crossrefs

Cf. A367039, A359807, A362248.