A381406 a(0) = 0; for n > 0, a(n) is the smallest unused number such that a(n) OR a(n-1) = 2^k - 1, where OR is the binary OR operation and k>=1, while the binary weight of a(n) does not equal that of a(n-1).

0, 1, 3, 2, 5, 7, 4, 11, 6, 13, 10, 15, 8, 23, 9, 14, 17, 30, 19, 12, 27, 20, 31, 16, 47, 18, 29, 22, 43, 21, 46, 25, 39, 24, 55, 26, 45, 50, 61, 34, 63, 28, 51, 44, 59, 36, 91, 37, 58, 69, 62, 33, 94, 35, 60, 67, 124, 71, 56, 79, 48, 95, 32, 127, 38, 57, 70, 121, 54, 41, 86, 107, 52, 75, 117, 42, 53, 74, 119, 40, 87, 104, 151, 105, 118, 73, 126, 49, 78, 115

Offset: 0

Author

Scott R. Shannon, Feb 22 2025

Keywords

• nonn
• base

Comments

The fixed points begin 0, 1, 10, 315, 413, 415, 1551, 1559, 1797; there are likely infinitely more.

Examples

			a(4) = 5 = 101_2 as 5 is unused and a(3) = 2 = 10_2, and 101_2 OR 10_2 = 111_2 = 2^3 - 1, while the binary weights of 5 and 2 are 2 and 1 respectively.
		

Links

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

Crossrefs

Cf. A000120, A086799, A061712, A057168, A381405.