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A078943 a(1)=1; a(n+1) is either a(n)-n or a(n)+n, where we choose the smallest one which is a positive integer that's not among the values a(1), ..., a(n). 3

%I

%S 1,2,4,7,3,8,14,21,13,22,12,23,11,24,10,25,9,26,44,63,43,64,42,19

%N a(1)=1; a(n+1) is either a(n)-n or a(n)+n, where we choose the smallest one which is a positive integer that's not among the values a(1), ..., a(n).

%C After a(24)=19, there are no more terms because a(24)-24 = -5 is not positive and a(24)+24 = 43 is equal to a(21).

%C If we only require that a(n+1) be either a(n)-n or a(n)+n, is there a sequence that contains every positive integer exactly once? I.e. can we take a walk on the positive integers, starting at 1 and always moving (either left or right) a distance n on the n-th step, so that we hit every positive integer exactly once?

%e a(9)=13, so a(10) is either 13-9=4 or 13+9=22. But 4 is not available since it equals a(3), so a(10)=22.

%Y Consists of terms 1 through 25 of A063733.

%K nonn,fini,full

%O 1,2

%A _Leroy Quet_, Dec 15 2002

%E Edited by _Dean Hickerson_, Dec 18 2002

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Last modified April 22 12:08 EDT 2021. Contains 343177 sequences. (Running on oeis4.)