A353242 Lexicographically earliest sequence of distinct nonnegative integers with alternating parity such that two consecutive terms have no common 1-bits in their binary expansions and a(2*n) = 2*a(n) for any n >= 0.

0, 1, 2, 9, 4, 33, 18, 5, 8, 17, 66, 25, 36, 65, 10, 37, 16, 13, 34, 73, 132, 257, 50, 129, 72, 21, 130, 41, 20, 161, 74, 133, 32, 69, 26, 289, 68, 265, 146, 97, 264, 49, 514, 137, 100, 145, 258, 45, 144, 261, 42, 81, 260, 169, 82, 385, 40, 149, 322, 513, 148

Offset

0,3

Comments

This sequence is a variant of A109812.

Terms of A004767 cannot appear in this sequence.

Links

Table of n, a(n) for n=0..60.

Rémy Sigrist, C++ program

Formula

a(2^k) = 2^k for any k >= 0.

Example

The first terms, alongside their binary expansions, are:
  n   a(n)  bin(a(n))
  --  ----  ---------
   0     0          0
   1     1          1
   2     2         10
   3     9       1001
   4     4        100
   5    33     100001
   6    18      10010
   7     5        101
   8     8       1000
   9    17      10001
  10    66    1000010
  11    25      11001
  12    36     100100
  13    65    1000001
  14    10       1010
  15    37     100101

Prog

(C++) See Links section.

Crossrefs

Cf. A109812, A004767.

Sequence in context: A220416 A054789 A002508 * A249596 A038215 A264110

Adjacent sequences: A353239 A353240 A353241 * A353243 A353244 A353245

Keyword

nonn,base

Author

Rémy Sigrist, Apr 08 2022

Status

approved