A262374 a(1) = 1; for n > 1, let s denote the binary representation of a(n-1) with the first bit omitted. Then a(n) is the smallest number not yet present whose binary representation starts with s, omitting leading zeros.

1, 2, 3, 4, 5, 6, 8, 7, 12, 9, 10, 11, 13, 20, 16, 14, 24, 17, 15, 28, 25, 18, 19, 26, 21, 22, 27, 23, 29, 52, 40, 32, 30, 56, 48, 33, 31, 60, 57, 50, 36, 34, 35, 49, 68, 37, 41, 38, 51, 39, 58, 53, 42, 43, 44, 96, 64, 45, 54, 88, 97, 66, 46, 59, 55, 47, 61

Offset: 1

Author

Allan C. Wechsler, Sep 20 2015

Keywords

• nonn
• base

Comments

It seems clear that every number will appear. It would be nice to have a formal proof. - N. J. A. Sloane, Sep 20 2015

Examples

			: 1                                      ...  1
:  10                                    ...  2
:    11                                  ...  3
:     100                                ...  4
:        101                             ...  5
:          110                           ...  6
:           1000                         ...  8
:               111                      ...  7
:                1100                    ... 12
:                 1001                   ...  9
:                    1010                ... 10
:                      1011              ... 11
:                        1101            ... 13
:                         10100          ... 20
:                           10000        ... 16
:                                1110    ... 14
:                                 11000  ... 24
:                                  10001 ... 17
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Binary counterpart of A262356.

A262381 gives the binary representations.

Cf. A262388.