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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.

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