A355065 Lexicographically earliest sequence of distinct positive integers such that if m and n are distinct and not coprime, then a(n) does not belong to the interval ceiling(a(m)/2)..2*a(m).

1, 2, 3, 5, 4, 11, 6, 23, 24, 47, 7, 95, 8, 191, 192, 383, 9, 767, 10, 1535, 1536, 3071, 12, 6143, 3072, 12287, 12288, 24575, 13, 49151, 14, 98303, 98304, 196607, 98305, 393215, 15, 786431, 786432, 1572863, 16, 3145727, 17, 6291455, 6291456, 12582911, 18

Offset: 1

Author

Rémy Sigrist, Jun 17 2022

Keywords

• nonn

Comments

This sequence is a permutation of the nonnegative integers (when n is prime, a(n) is the least value not yet in the sequence).

The inverse sequence (A355066) has similarities with the Two-Up sequence (A090252) as A355066(n) is coprime to the next n terms (and to the floor(n/2) previous terms).

Note that the relation "u does not belong to the interval ceiling(v/2)..2*v" is symmetrical (for u, v > 0).

Examples

			The first terms, alongside the forbidden values, are:
  n   a(n)  Forbidden values
  --  ----  ---------------------------------------------------
   1     1  None
   2     2  None
   3     3  None
   4     5  1..4 (from m=2)
   5     4  None
   6    11  1..4 (from m=2), 2..6 (from m=3), 3..10 (from m=4)
   7     6  None
   8    23  1..4 (from m=2), 3..10 (from m=4), 6..22 (from m=6)
   9    24  2..6 (from m=3), 6..22 (from m=6)
  10    47  1..4 (from m=2), 3..10 (from m=4), 2..8 (from m=5),
            6..22 (from m=6), 12..46 (from m=8)
  11     7  None
		

Links

• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A090252, A355066 (inverse).

Programs

PARI

See Links section.