A230599 -id:A230599 - cp's OEIS frontend

A230598 Lexicographically earliest sequence of distinct positive integers such that all black pixels in the binary plot of the sequence are connected (see Comments for details).

1, 3, 2, 6, 4, 5, 7, 9, 11, 10, 14, 8, 12, 13, 15, 17, 19, 18, 22, 20, 21, 23, 25, 27, 26, 30, 16, 24, 28, 29, 31, 33, 35, 34, 38, 36, 37, 39, 41, 43, 42, 46, 40, 44, 45, 47, 49, 51, 50, 54, 52, 53, 55, 57, 59, 58, 62, 32, 48, 56, 60, 61, 63, 65, 67, 66, 70

Offset: 1

Paul Tek, Oct 24 2013

For any n, m, i, j such that a(n) AND (2^i) <> 0, and a(m) AND (2^j) <>0 (where AND stands for the bitwise AND operator), there exist two sequences of finite length L, say p and b, such that:
(1) p(1)=n, b(1)=i,
(2) p(L)=m, b(L)=j,
(3) a(p(k)) AND (2^b(k)) <> 0 for any k between 1 and L,
(4) |p(k+1)-p(k)| + |b(k+1)-b(k)| = 1 for any k between 1 and L-1.
These two finite sequences define a path of black pixels connecting the black pixels at positions (n,i) and (m,j).

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, Binary plot of the first 127 terms
Paul Tek, PERL program for this sequence
Eric Weisstein's World of Mathematics, Binary Plot
Index entries for sequences that are permutations of the natural numbers

Cf. A226077, A230599.

Perl
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See Link section.
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Empirically, for any k>2 :
(1) a(2^k-1) = 2^k-1,
(2) a(2^k) = 2^k+1,
(3) a(n) = a(n-2^k+1) + 2^k, for any n such that 2^k<=n<2^(k+1)-(k+1),
(4) a(n) = 2^k, for n=2^(k+1)-(k+1),
(5) a(n) = a(n-2^k) + 2^k, for any n such that 2^(k+1)-(k+1)

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A230598 Lexicographically earliest sequence of distinct positive integers such that all black pixels in the binary plot of the sequence are connected (see Comments for details).

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