A375889 - OEIS

A375889

a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest unused positive number such that a(n) shares a factor with a(n-1) and (a(n) AND a(n-1)) = min(a(n), a(n-1)), where AND is the binary AND operation.

1, 3, 15, 5, 45, 9, 27, 18, 2, 6, 4, 12, 8, 10, 14, 30, 16, 20, 22, 54, 32, 34, 38, 36, 39, 33, 51, 17, 85, 65, 75, 66, 64, 68, 70, 78, 72, 74, 90, 24, 26, 58, 40, 42, 46, 44, 60, 28, 62, 48, 50, 55, 35, 63, 7, 119, 21, 87, 69, 93, 81, 117, 52, 116, 80, 82, 86, 84, 92, 76, 94, 88, 120, 56, 122, 96

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OFFSET

1,2

COMMENTS

The fixed points begin 1, 12, 284, 50726, 50764, 50770, 50772, 50811, although there are likely more.

The sequence is conjectured to be a permutation of the positive integers.

LINKS

Scott R. Shannon, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) = 5 as 5 shares a factor with a(3) = 15 and min(15,5) = 5 and (5 AND 15) = 101_2 AND 1111_2 = 101_2 = 5.

CROSSREFS

Cf. A375890, A303767, A169837, A027750.