

A344184


Lexicographically earliest sequence of positive integers such that for any n > 0, the binary expansion of a(n) contains the binary expansion of k for k = 1..n and the binary expansion of a(n+1) is obtained by replacing a possibly empty substring of the binary expansion of a(n) by the binary expansion of n+1.


1



1, 2, 6, 12, 44, 44, 92, 184, 1208, 1336, 5304, 5304, 10680, 10680, 21368, 42736, 567024, 673520, 5383920, 5383920, 21535472, 172283632, 172283632, 172283632, 344774384, 344774384, 344774384, 344774384, 689559280, 689559280, 1379118576, 2758237152, 71477713888
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OFFSET

1,2


COMMENTS

This sequence is a variant of A056744, easier to compute.
This sequence is not weakly increasing; a(109) < a(108).


LINKS



FORMULA



EXAMPLE

The first terms, alongside their binary expansion, are:
n a(n) bin(n) bin(a(n))
   
1 1 1 1
2 2 10 10
3 6 11 110
4 12 100 1100
5 44 101 101100
6 44 110 101100
7 92 111 1011100
8 184 1000 10111000
9 1208 1001 10010111000
10 1336 1010 10100111000
11 5304 1011 1010010111000
12 5304 1100 1010010111000
13 10680 1101 10100110111000
14 10680 1110 10100110111000
15 21368 1111 101001101111000


PROG

(PARI) See Links section.


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



