A338502 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(1) XOR ... XOR a(n) is a square (where XOR denotes the bitwise XOR operator).

0, 1, 5, 4, 9, 8, 17, 16, 25, 24, 37, 21, 33, 20, 13, 45, 32, 29, 40, 48, 65, 36, 53, 72, 61, 52, 80, 57, 93, 64, 85, 49, 81, 88, 56, 96, 117, 100, 68, 125, 105, 116, 101, 120, 112, 73, 89, 137, 84, 109, 141, 180, 113, 133, 160, 132, 161, 152, 121, 144, 128

Offset: 1

Author

Rémy Sigrist, Oct 31 2020

Keywords

• nonn
• base

Comments

All terms belong to A042948.

Examples

			The first terms, alongside a(1) XOR ... XOR a(n), are:
  n   a(n)  a(1) AND ... AND a(n)
  --  ----  ---------------------
   1     0                0 = 0^2
   2     1                1 = 1^2
   3     5                4 = 2^2
   4     4                0 = 0^2
   5     9                9 = 3^2
   6     8                1 = 1^2
   7    17               16 = 4^2
   8    16                0 = 0^2
   9    25               25 = 5^2
  10    24                1 = 1^2
  11    37               36 = 6^2
  12    21               49 = 7^2
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A338502

Crossrefs

Cf. A042948, A042964, A292388 (prime variant), A338503.

Programs

PARI

See Links section.