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 A305369 Lexicographically earliest sequence of distinct positive integers such that for each 1 in the binary expansion of a(n), exactly one of a(n-1) and a(n+1) has a 1 in the same position. 6
 1, 3, 2, 4, 5, 9, 8, 6, 7, 17, 16, 10, 11, 21, 20, 32, 33, 13, 12, 18, 19, 37, 36, 24, 25, 35, 34, 28, 29, 65, 64, 14, 15, 49, 48, 66, 67, 41, 40, 22, 23, 73, 72, 38, 39, 81, 80, 42, 43, 69, 68, 26, 27, 97, 96, 30, 31, 129, 128, 44, 45, 83, 82, 132, 133, 51, 50, 76, 77, 131, 130, 52, 53, 75, 74, 144, 145, 47, 46, 192 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is to A280864 as A115510 is to A064413 (EKG) and A252867 is to A098550 (Yellowstone). REFERENCES Empirical: a(4k) = 2*Q(2k), a(4k+1) = a(4k)+1, a(4k+2) = 2*Q(2k+1)+1, a(4k+3) = 2*Q(2k+1), where Q (for Quet) is A109812. Since Q has a simpler definition, there is hope for a proof of this connection. LINKS N. J. A. Sloane, Table of n, a(n) for n = 1..10000 N. J. A. Sloane, Maple program EXAMPLE After a(1) = 1, a(2) is the smallest missing odd number, so a(2) = 3. a(3) is then the smallest missing number of the form ...1*_2, so a(3) = 10_2 = 2. After a(15) = 20 = 10100_2, a(16) is the smallest missing number of the form ...0*0**_2, which is 100000_2 = 32. CROSSREFS Cf. A280864, A252867, A098550, A115510, A064413, A109812. The graphs of A109812, A252867, A305369, A305372 all have roughly the same, mysterious, fractal-like structure. - N. J. A. Sloane, Jun 03 2018 Sequence in context: A086962 A001612 A275901 * A097092 A241417 A211363 Adjacent sequences:  A305366 A305367 A305368 * A305370 A305371 A305372 KEYWORD nonn,look AUTHOR N. J. A. Sloane, Jun 02 2018 STATUS approved

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)