

A188215


Starting with an empty list, n is inserted after the a(n)th element such that the binary representations of the list's elements are always sorted lexicographically.


2



0, 1, 2, 3, 3, 4, 6, 7, 4, 5, 7, 8, 11, 12, 14, 15, 5, 6, 8, 9, 12, 13, 15, 16, 20, 21, 23, 24, 27, 28, 30, 31, 6, 7, 9, 10, 13, 14, 16, 17, 21, 22, 24, 25, 28, 29, 31, 32, 37, 38, 40, 41, 44, 45, 47, 48, 52, 53, 55
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OFFSET

0,3


COMMENTS

The last occurrence of any positive n in this sequence is a(2^(n  1)).
As the list in question expands, its initial terms converge toward A131577.
The last item of the list is always zero or an element of A075427.


LINKS



FORMULA

a(2^n + b) = n + b + 1 for b = 0 or 1.
a(2^n  b) = 2^n  b for b = 1 or 2.


EXAMPLE

For example, an a(n) of 3 means that n should be inserted after the 3rd element of the list to keep the elements lexicographically ordered.
[] (Initial empty list)
[0] (Zero inserted at the beginning: a(0) = 0)
[0, 1] (One inserted after element 1: a(1) = 1)
[0, 1, 10] (Two inserted after element 2: a(2) = 2)
[0, 1, 10, 11] (Three inserted after element 3: a(3) = 3)
[0, 1, 10, 100, 11] (Four inserted after element 3: a(4) = 3)


MATHEMATICA

lst = {}; Table[s = IntegerString[n, 2]; lst = Sort[Append[lst, s]]; Position[lst, s][[1, 1]]  1, {n, 0, 63}] (* T. D. Noe, Apr 19 2011 *)


PROG

(Python)
l = []
for i in range(17):
b = bin(i)[2:]
l.append(b)
l.sort()
print(l.index(b))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



