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

1,2

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

Links

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

Example

: 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

Crossrefs

Binary counterpart of A262356.

A262381 gives the binary representations.

Cf. A262388.

Sequence in context: A232895 A274607 A339607 * A299442 A299440 A330401

Adjacent sequences: A262371 A262372 A262373 * A262375 A262376 A262377

Keyword

nonn,base

Author

Allan C. Wechsler, Sep 20 2015

Status

approved