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A333210 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)+a(n-m) = a(n-1)+a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

%I A333210 #16 Mar 12 2020 02:59:28
%S A333210 0,0,0,1,0,1,1,0,2,2,0,2,1,0,6,0,1,3,8,0,0,18,0,1,7,5,0,0,7,0,1,7,7,0,
%T A333210 4,17,0,0,10,0,1,10,23,0,0,7,12,0,22,0,1,10,10,0,14,22,0,7,12,12,0,13,
%U A333210 0,1,13,10,22,0,11,17,0,34,0,1,10,6,0,61,0,1,6,23,0,17,13,0,23,4,0,54,0,1,12
%N A333210 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)+a(n-m) = a(n-1)+a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.
%C A333210 After 100 million terms the smallest number not appearing is 381884, while the smallest sum of adjacent terms not appearing is 487833.
%H A333210 Scott R. Shannon, <a href="/A333210/b333210.txt">Table of n, a(n) for n = 1..10000</a>.
%H A333210 Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=etMJxB-igrc">Don't Know (the Van Eck Sequence)</a>, Numberphile video (2019).
%e A333210 a(3) = 0 as a(1)+a(2) = 0+0 = 0, which has not previously appeared as the sum of two adjacent terms.
%e A333210 a(4) = 1 as a(2)+a(3) = 0+0 = 0, which equals the sum a(1)+a(2), one term back from a(3).
%e A333210 a(5) = 0 as a(3)+a(4) = 0+1 = 1, which has not previously appeared as the sum of two adjacent terms.
%e A333210 a(6) = 1 as a(4)+a(5) = 1+0 = 1, which equals the sum a(3)+a(4), one term back from a(5).
%e A333210 a(19) = 8 as a(17)+a(18) = 1+3 = 4, which equals the sum a(9)+a(10), eight terms back from a(18).
%Y A333210 Cf. A181391, A171898, A308721, A333211.
%K A333210 nonn
%O A333210 1,9
%A A333210 _Scott R. Shannon_, Mar 11 2020