A306866 Lexicographically earliest sequence of distinct positive terms such that the binary representation of the sum of two consecutive terms has at most 2 runs of ones.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 13, 14, 15, 16, 17, 18, 20, 19, 21, 23, 24, 22, 25, 26, 28, 27, 29, 30, 31, 32, 33, 34, 36, 35, 37, 39, 40, 38, 41, 47, 45, 43, 49, 46, 42, 50, 44, 48, 51, 52, 56, 54, 57, 53, 55, 58, 60, 59, 61, 62, 63, 64, 65, 66, 68

Offset

1,2

Comments

This sequence is a variant of A306865.

This sequence is likely a permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, PARI program for A306866

Formula

A069010(a(n) + a(n+1)) <= 2.

Example

The first terms,
  n   a(n)  a(n)+a(n+1)  bin(a(n)+a(n+1))
  --  ----  -----------  ----------------
   1     1            3                11
   2     2            5               101
   3     3            7               111
   4     4            9              1001
   5     5           11              1011
   6     6           13              1101
   7     7           15              1111
   8     8           17             10001
   9     9           19             10011
  10    10           22             10110
  11    12           23             10111
  12    11           24             11000
  13    13           27             11011
  14    14           29             11101
  15    15           31             11111
  16    16           33            100001

Prog

(PARI) See Links section.

Crossrefs

Cf. A069010, A306865.

Sequence in context: A239235 A031297 A239086 * A187769 A357492 A209862

Adjacent sequences: A306863 A306864 A306865 * A306867 A306868 A306869

Keyword

nonn,base,look

Author

Rémy Sigrist, Mar 14 2019

Status

approved