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A333211 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 A333211 #12 Mar 12 2020 02:59:24
%S A333211 0,0,0,1,1,0,2,1,0,2,1,3,0,3,1,3,1,1,13,0,6,1,0,2,1,14,0,3,1,12,0,3,1,
%T A333211 4,0,3,1,4,4,0,4,1,4,1,1,27,0,6,1,27,4,0,4,1,10,0,3,1,21,0,3,1,4,9,0,
%U A333211 4,1,4,1,1,25,0,6,1,25,4,0,4,1,10,25
%N A333211 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 A333211 After 100 million terms the smallest number not appearing is 179549, while the smallest product of adjacent terms not appearing is 2969.
%H A333211 Scott R. Shannon, <a href="/A333211/b333211.txt">Table of n, a(n) for n = 1..10000</a>.
%H A333211 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 A333211 a(3) = 0 as a(1)*a(2) = 0*0 = 0, which has not previously appeared as the product of two adjacent terms.
%e A333211 a(4) = 1 as a(2)*a(3) = 0*0 = 0, which equals the product a(1)*a(2), one term back from a(3).
%e A333211 a(5) = 1 as a(3)*a(4) = 0*1 = 0, which equals the product a(2)*a(3), one term back from a(3).
%e A333211 a(6) = 0 as a(4)*a(5) = 1*1 = 1, which has not previously appeared as the product of two adjacent terms.
%e A333211 a(19) = 13 as a(17)*a(18) = 1*1 = 1, which equals the product a(4)*a(5), thirteen terms back from a(18).
%Y A333211 Cf. A181391, A171898, A308721, A333210.
%K A333211 nonn
%O A333211 1,7
%A A333211 _Scott R. Shannon_, Mar 11 2020