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%I #22 Nov 04 2023 13:49:36
%S 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,
%T 26,28,28,28,31,32,32,32,32,32,32,38,39,40,41,42,42,44,44,46,46,48,48,
%U 48,51,52,52,52,55,56,56,56,56,60,61,62,62,64,64,64,64,64,64,64
%N 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.
%C It appears that A085262 gives the distinct values of this sequence (except for the initial zero).
%C The sequence is nondecreasing.
%H Neal Gersh Tolunsky, <a href="/A367039/b367039.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%e 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):
%e 0, 1, 2, 2, 4, 4, 4
%e 0<-1
%e 0, 1, 2, 2, 4, 4, 4
%e 1<----2
%e 0, 1, 2, 2, 4, 4, 4
%e 1->2<----------4
%e 0, 1, 2, 2, 4, 4, 4
%e ?
%e 0, 1, 2, 2, 4, 4, 4
%e 2---->4
%e 0, 1, 2, 2, 4, 4, 4
%e 2---->4
%e 0, 1, 2, 2, 4, 4, 4
%e ?
%Y Cf. A359807, A085262, A367026.
%K nonn
%O 1,3
%A _Neal Gersh Tolunsky_, Nov 02 2023
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