A375828 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that (a(n-1) AND a(n)) = a(n-1) if a(n-1) is prime, otherwise (a(n-1) AND a(n)) = 0, where AND is the binary AND operation.

1, 2, 3, 7, 15, 16, 4, 8, 5, 13, 29, 31, 63, 64, 6, 9, 18, 12, 17, 19, 23, 55, 72, 20, 10, 21, 32, 11, 27, 36, 24, 33, 14, 48, 65, 22, 40, 66, 25, 34, 28, 35, 68, 26, 37, 39, 80, 38, 73, 75, 52, 67, 71, 79, 95, 128, 30, 96, 129, 42, 69, 50, 76, 49, 70, 41, 43, 47, 111, 144, 44, 81, 46, 145, 74, 53, 61, 125, 130, 45, 82, 132, 51, 136, 54, 137, 139, 143, 112

Offset

1,2

Comments

The terms form a pattern similar to that in A109812. In the first 250000 terms the fixed points are 1, 2, 3, 8, 3650, 50624, 203074. 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

Scott R. Shannon, Image of the first 250000 terms. The green line is a(n) = n.

Example

a(5) = 15 as a(4) = 7 = 111_2 is prime, and ((15 = 1111_2) AND 111_2) = 111_2 = 7.
a(6) = 16 as a(5) = 15 = 1111_2 is not prime, and ((16 = 10000_2) AND 1111_2) = 0.

Crossrefs

Cf. A375829, A109812, A007088, A115510, A000040, A353989.

Sequence in context: A271718 A222626 A006627 * A077161 A068080 A276600

Adjacent sequences: A375825 A375826 A375827 * A375829 A375830 A375831

Keyword

nonn

Author

Scott R. Shannon, Aug 30 2024

Status

approved