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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.
4
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
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
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Nov 02 2023
STATUS
approved