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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.
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%I #12 Mar 12 2020 02:59:24

%S 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 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 4,1,4,1,1,25,0,6,1,25,4,0,4,1,10,25

%N 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 After 100 million terms the smallest number not appearing is 179549, while the smallest product of adjacent terms not appearing is 2969.

%H Scott R. Shannon, <a href="/A333211/b333211.txt">Table of n, a(n) for n = 1..10000</a>.

%H 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 a(3) = 0 as a(1)*a(2) = 0*0 = 0, which has not previously appeared as the product of two adjacent terms.

%e 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 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 a(6) = 0 as a(4)*a(5) = 1*1 = 1, which has not previously appeared as the product of two adjacent terms.

%e 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 Cf. A181391, A171898, A308721, A333210.

%K nonn

%O 1,7

%A _Scott R. Shannon_, Mar 11 2020