A360363 Lexicographically earliest sequence of distinct positive integers such that the bitwise XOR of two distinct terms are all distinct.
1, 2, 3, 4, 8, 12, 16, 32, 48, 64, 85, 106, 128, 150, 171, 216, 237, 247, 256, 279, 297, 452, 512, 537, 558, 594, 640, 803, 860, 997, 1024, 1051, 1069, 1115, 1169, 1333, 1345, 1620, 1866, 2048, 2077, 2086, 2159, 2257, 2363, 2446, 2737, 2860, 3212, 3335, 3761
Offset: 1
Examples
The first terms are: n a(n) a(k) XOR a(n) (for k = 1..n-1) -- ---- ---------------------------------------------------------- 1 1 N/A 2 2 3 3 3 2, 1 4 4 5, 6, 7 5 8 9, 10, 11, 12 6 12 13, 14, 15, 8, 4 7 16 17, 18, 19, 20, 24, 28 8 32 33, 34, 35, 36, 40, 44, 48 9 48 49, 50, 51, 52, 56, 60, 32, 16 10 64 65, 66, 67, 68, 72, 76, 80, 96, 112 11 85 84, 87, 86, 81, 93, 89, 69, 117, 101, 21 12 106 107, 104, 105, 110, 98, 102, 122, 74, 90, 42, 63 13 128 129, 130, 131, 132, 136, 140, 144, 160, 176, 192, 213, 234
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, C++ program
Programs
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Python
from itertools import islice def agen(): # generator of terms aset, xset, k = set(), set(), 0 while True: k += 1 while any(k^an in xset for an in aset): k += 1 yield k; xset.update(k^an for an in aset); aset.add(k) print(list(islice(agen(), 51))) # Michael S. Branicky, Feb 05 2023
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