A395189 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n > 2, a(n) shares a factor with a(n-1) and R(a(n),2) shares a factor with R(a(n-1),2), where R(k,2) is the digital reversal of the binary value of k, read in binary.

1, 3, 6, 9, 12, 15, 5, 10, 20, 30, 18, 21, 7, 14, 28, 35, 42, 24, 27, 33, 36, 39, 45, 40, 38, 19, 76, 60, 48, 51, 17, 34, 68, 85, 65, 75, 54, 57, 63, 49, 56, 70, 84, 66, 26, 13, 52, 104, 118, 59, 236, 80, 90, 69, 72, 78, 50, 25, 100, 125, 95, 105, 81, 87, 93, 31, 62

Offset

1,2

Comments

As the sequence is infinite no term, except a(1), can be a power of 2.

In the first 100000 terms the fixed points are 1, 14, 728 and 2987, although more likely exist.

Links

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

Scott R. Shannon, Image of the first 100000 terms. The thin green line is a(n) = n.

Example

a(10) = 30 as 30 is unused, shares a factor with a(9) = 20, and R(30,2) = R(11110_2,2) = 1111_2 = 15 shares a factor with R(20,2) = R(10100_2,2) = 101_2 = 5.

Crossrefs

Cf. A395077 (base 10), A305989, A007088, A064413, A393075, A393176.

Sequence in context: A226894 A359213 A393075 * A091780 A331060 A329514

Adjacent sequences: A395186 A395187 A395188 * A395190 A395191 A395192

Keyword

nonn,base

Author

Scott R. Shannon, Apr 15 2026

Status

approved