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%I #19 Mar 27 2022 15:13:48
%S 0,1,2,5,10,4,8,20,9,6,33,18,32,14,96,3,48,7,16,11,80,12,64,13,66,17,
%T 34,21,40,65,42,68,24,69,26,36,130,37,74,49,72,52,136,19,128,22,160,
%U 15,192,23,224,25,288,27,100,129,260,131,28,35,76,161,84,162,88
%N a(0)=0, a(1)=1, a(2)=2; thereafter, a(n) is smallest number m not yet in the sequence such that the binary expansions of m and a(n-2) have a 1 in common, but the 1's in m are disjoint from the 1's in a(n-1) and a(n-3).
%C A set-theory analog of A350359. This has the same relationship to A350359 as A115510 does to the EKG sequence A064413, as A252867 does to the Yellowstone permutation A098550, and as A338833 does to the Enots Wolley sequence A336957.
%C An equivalent definition in terms of sets: S(0) = {}, S(1) = {1}, S(2} = {1,2}; thereafter S(n) is the smallest set (different from the S{i} already defined) of positive integers such that S(n) meets S(n-2) but is disjoint from S(n-1) and S(n-3}.
%H Rémy Sigrist, <a href="/A352199/b352199.txt">Table of n, a(n) for n = 0..10000</a>
%e After a(4) = 10 = 1010_2, a(5) = 4 = 100_2, a(6) = 8 = 1000_2, a(7) must have the form ...?010?_2, and the smallest missing number of that form is 20 = 10100_2 = 20.
%o (PARI) { s=0; for (n=1, #a=vector(65), if (n<=3, a[n]=n-1, for (v=0, oo, if (!bittest(s,v) && bitand(v,a[n-2]) && !bitand(v,bitor(a[n-3],a[n-1])), a[n]=v; break))); s+=2^a[n]; print1(a[n]", ")) } \\ _Rémy Sigrist_, Mar 27 2022
%Y Cf. A064413, A098550, A115510, A252867, A338833, A350359.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Mar 26 2022
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