A375829 -id:A375829 - cp's OEIS frontend

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

Scott R. Shannon, Aug 30 2024

nonn

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.

			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.

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.

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

cp's OEIS Frontend

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.

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