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

1,3

Links

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

Example

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

Prog

(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)))

Crossrefs

See A308057 and A308058 for variants.

Sequence in context: A007381 A366877 A337377 * A361026 A319698 A096234

Adjacent sequences: A308056 A308057 A308058 * A308060 A308061 A308062

Keyword

nonn,look,base

Author

Rémy Sigrist, May 10 2019

Status

approved