A338500 Lexicographically earliest sequence of distinct nonnegative terms such that for any n >= 0, a(n) AND a(n+1) is a square (where AND denotes the bitwise AND operator).

0, 1, 2, 4, 3, 5, 6, 8, 7, 9, 11, 13, 16, 10, 17, 12, 18, 20, 14, 21, 24, 19, 28, 32, 15, 25, 22, 33, 23, 36, 26, 37, 27, 29, 34, 64, 30, 48, 31, 41, 65, 35, 68, 38, 44, 39, 52, 45, 54, 69, 40, 66, 49, 51, 53, 46, 80, 42, 81, 43, 73, 47, 84, 50, 72, 55, 57, 67

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers with inverse A334672:

- we can always extend the sequence with a power of 4,

- eventually every power of 4 appears in the sequence,

- a power of 4 is followed by the least value not yet in the sequence,

- so eventually every integer will appear.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program for A338500

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside a(n) AND a(n+1), are:
  n   a(n)  a(n) AND a(n+1)
  --  ----  ---------------
   0     0              0^2
   1     1              0^2
   2     2              0^2
   3     4              0^2
   4     3              1^2
   5     5              2^2
   6     6              0^2
   7     8              0^2
   8     7              1^2
   9     9              3^2
  10    11              3^2
  11    13              0^2
  12    16              0^2

Prog

(PARI) See Links section.

Crossrefs

Cf. A334672 (inverse), A335615, A338501.

Sequence in context: A107896 A107897 A133256 * A259570 A334672 A095690

Adjacent sequences: A338497 A338498 A338499 * A338501 A338502 A338503

Keyword

nonn,base

Author

Rémy Sigrist, Oct 31 2020

Status

approved