cp's OEIS Frontend

A352199 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).

%I A352199 #23 Dec 25 2024 04:03:51
%S A352199 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 A352199 34,21,40,65,42,68,24,69,26,36,130,37,74,49,72,52,136,19,128,22,160,
%U A352199 15,192,23,224,25,288,27,100,129,260,131,28,35,76,161,84,162,88
%N A352199 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 A352199 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 A352199 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 A352199 Rémy Sigrist, <a href="/A352199/b352199.txt">Table of n, a(n) for n = 0..10000</a>
%e A352199 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 A352199 (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 A352199 Cf. A064413, A098550, A115510, A252867, A338833, A350359.
%K A352199 nonn,base
%O A352199 0,3
%A A352199 _N. J. A. Sloane_, Mar 26 2022