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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). 1
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, 34, 21, 40, 65, 42, 68, 24, 69, 26, 36, 130, 37, 74, 49, 72, 52, 136, 19, 128, 22, 160, 15, 192, 23, 224, 25, 288, 27, 100, 129, 260, 131, 28, 35, 76, 161, 84, 162, 88 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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.
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}.
LINKS
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A177356 A078322 A252867 * A194356 A227317 A224300
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Mar 26 2022
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)