A288139 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight <= 4.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 22, 23, 25, 24, 26, 27, 29, 28, 30, 34, 31, 33, 32, 35, 36, 37, 38, 39, 41, 40, 42, 43, 45, 44, 46, 50, 47, 49, 48, 51, 53, 52, 54, 58, 55, 57, 56, 60, 68, 61, 59, 69, 62, 66, 63, 65

Offset

1,2

Comments

Conjecturally, this is a permutation of the natural numbers.

This sequence has connections with A287639: here we have an upper bound, there a lower bound, on the Hamming weight of the sum of two consecutive terms.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..16384

Rémy Sigrist, PARI program for A288139

Example

The first terms, alongside a(n)+a(n+1) in binary and its Hamming weight are:
n       a(n)    a(n)+a(n+1)       Hamming weight
--      ----    -----------       --------------
1       1                11       2
2       2               101       2
3       3               111       3
4       4              1001       2
5       5              1011       3
6       6              1101       3
7       7              1111       4
8       8             10001       2
9       9             10011       3
10      10            10101       3
11      11            10111       4
12      12            11001       3
13      13            11011       4
14      14            11101       4
15      15           100000       1
16      17           100001       2
17      16           100010       2
18      18           100101       3
19      19           100111       4
20      20           101001       3

Crossrefs

Cf. A000120, A287639.

Sequence in context: A357979 A023797 A032951 * A194897 A140823 A209061

Adjacent sequences: A288136 A288137 A288138 * A288140 A288141 A288142

Keyword

nonn,look,base

Author

Rémy Sigrist, Jun 17 2017

Status

approved