A381405 a(0) = 0; for n > 0, a(n) is the smallest unused number such that a(n) AND a(n-1) = 0, where AND is the binary AND operation, while the binary weight of a(n) does not equal that of a(n-1).

0, 1, 6, 8, 3, 4, 9, 2, 5, 16, 7, 24, 32, 10, 21, 34, 13, 18, 37, 64, 11, 20, 35, 12, 19, 36, 25, 66, 28, 33, 14, 17, 38, 65, 22, 40, 23, 72, 39, 80, 15, 48, 67, 60, 128, 26, 68, 27, 96, 29, 98, 129, 30, 97, 130, 41, 86, 136, 49, 78, 144, 42, 85, 138, 53, 74, 132, 43, 84, 139, 52, 75, 148, 99, 140, 51, 76, 147, 44, 83, 160, 31, 192, 45, 82, 141, 50, 77, 146, 101

Offset

0,3

Comments

In the first 100000 terms the fixed points are 0, 1, 28, 76, 543, 1580, although more likely exist.

Links

Scott R. Shannon, Table of n, a(n) for n = 0..10000

Example

a(3) = 8 = 1000_2 as 8 is unused and a(2) = 6 = 110_2, and 1000_2 AND 110_2 = 0 while the binary weights of 8 and 6 are 1 and 2 respectively.

Crossrefs

Cf. A000120, A129760, A061712, A057168, A381406.

Sequence in context: A097880 A196768 A355976 * A021598 A021940 A316256

Adjacent sequences: A381402 A381403 A381404 * A381406 A381407 A381408

Keyword

nonn,base

Author

Scott R. Shannon, Feb 22 2025

Status

approved