A308059 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) XOR (2*a(m+1)) <> a(n) XOR (2*a(n+1)) (where XOR denotes the bitwise XOR operator).

1, 1, 2, 1, 3, 1, 4, 1, 5, 4, 3, 6, 1, 8, 1, 9, 8, 2, 5, 8, 3, 10, 8, 8, 10, 10, 12, 12, 13, 8, 12, 16, 16, 17, 5, 13, 16, 18, 18, 20, 20, 21, 16, 20, 24, 24, 25, 16, 24, 27, 16, 25, 18, 26, 32, 32, 33, 1, 16, 32, 34, 34, 36, 36, 37, 1, 18, 32, 36, 40, 40, 41

Offset: 1

Author

Rémy Sigrist, May 10 2019

Keywords

• nonn
• look
• base

Examples

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

Links

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

Crossrefs

See A308057 and A308058 for variants.

Programs

PARI

s=0; v=1; for(n=1, 72, print1(v", "); for (w=1, oo, if (!bittest(s,x=bitxor(v,2*w)), s+=2^x; v=w; break)))