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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).
2
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
1,2
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).
EXAMPLE
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
PROG
(PARI) See Links section.
CROSSREFS
Cf. A090252, A355066 (inverse).
Sequence in context: A370895 A112060 A084933 * A213900 A213648 A302849
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 17 2022
STATUS
approved