A085262 -id:A085262 - cp's OEIS frontend

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

Neal Gersh Tolunsky, Nov 02 2023

nonn

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

The sequence is nondecreasing.

			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
                  ?

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

Cf. A359807, A085262, A367026.

A085246 Satisfies a(1)=1, a(A026835(n+1)) = a(n)+1, with a(m)=0 for all m not found in A026835, where A026835(n+2)=A026835(n+1)+a(n)+1.

Original entry on oeis.org

1, 2, 0, 3, 0, 0, 1, 4, 0, 0, 0, 1, 1, 2, 0, 5, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 3, 0, 0, 1, 6, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 2, 0, 2, 0, 3, 0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 0, 1, 1, 2, 0, 7, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 3, 0, 0, 1, 3, 0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 0, 1, 1, 2, 0, 4, 0

Offset: 1

Paul D. Hanna, Aug 22 2003

nonn

Removing the leading '1' and all zeros results in the original sequence with every term incremented by 1.

			Initialize all terms to zero. Set a(1)=1, go one term forward,
set a(2)=a(1)+1=2, go 2 terms forward,
set a(4)=a(2)+1=3, go 3 terms forward,
set a(7)=a(3)+1=1, go 1 term forward,
set a(8)=a(4)+1=4, go 4 terms forward,
set a(12)=a(5)+1=1, etc.
The indices 1,2,4,7,8,12,... form A085262.

Cf. A085262.

Records occur at 2^n: a(2^n)=n+1.

cp's OEIS Frontend

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.

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