

A305369


Lexicographically earliest sequence of distinct positive integers such that for each 1 in the binary expansion of a(n), exactly one of a(n1) 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
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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, fractallike 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



