A190126 Numbers 1 through 10000 sorted lexicographically in binary representation.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 8193, 4097, 8194, 8195, 2049, 4098, 8196, 8197, 4099, 8198, 8199, 1025, 2050, 4100, 8200, 8201, 4101, 8202, 8203, 2051, 4102, 8204, 8205, 4103, 8206, 8207, 513, 1026, 2052, 4104, 8208, 8209, 4105

Offset

1,2

Comments

A190127 = inverse permutation: a(A190127(n)) = A190127(a(n)) = n;

a(n) <> n for n > 2.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (full sequence)

Eric Weisstein's World of Mathematics, Lexicographic Order.

Wikipedia, Lexicographical order.

Index entries for sequences related to binary expansion of n

Example

a(13) = 4096 -> 1000000000000  [bin];
a(14) = 8192 -> 10000000000000 [bin];
a(15) = 8193 -> 10000000000001 [bin];
a(16) = 4097 -> 1000000000001  [bin];
a(17) = 8194 -> 10000000000010 [bin];
a(18) = 8195 -> 10000000000011 [bin];
a(19) = 2049 -> 100000000001   [bin];
a(20) = 4098 -> 1000000000010  [bin];
largest term a(3626) = 10000 -> 10011100010000 [bin];
last term a(10000) = 8191 -> 1111111111111 [bin], largest term lexicographically.

Prog

(Haskell)
import Data.Ord (comparing)
import Data.List (sortBy)
a190126 n = a190126_list !! (n-1)
a190126_list = sortBy (comparing (show . a007088)) [1..10000]

Crossrefs

Cf. A007088; A190128 (base 3), A190130 (base 8), A190016 (base 10), A190132 (base 12), A190134 (base 16).

Sequence in context: A168084 A133025 A216095 * A219676 A220469 A370254

Adjacent sequences: A190123 A190124 A190125 * A190127 A190128 A190129

Keyword

nonn,base,fini,full

Author

Reinhard Zumkeller, May 06 2011

Status

approved