A352713 Lexicographically earliest sequence of distinct nonnegative integers such that the binary expansions of two consecutive terms have no common 1, and the least value not yet in the sequence appears as soon as possible.
0, 1, 2, 4, 3, 8, 5, 16, 6, 24, 7, 32, 9, 20, 10, 36, 11, 48, 12, 18, 13, 64, 14, 80, 15, 96, 17, 40, 19, 72, 21, 104, 22, 128, 23, 160, 25, 68, 26, 100, 27, 192, 28, 34, 29, 224, 30, 256, 31, 320, 33, 76, 35, 88, 37, 136, 38, 144, 39, 208, 41, 84, 42, 132, 43
Offset: 0
Examples
The first terms are (stars correspond to "w" terms): n a(n) bin(a(n)) w -- ---- --------- - 0 0 0 1 1 1 2 2 10 3 4 100 * 4 3 11 5 8 1000 * 6 5 101 7 16 10000 * 8 6 110 9 24 11000 * 10 7 111 11 32 100000 * 12 9 1001 13 20 10100 * 14 10 1010 15 36 100100 *
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
- Rémy Sigrist, Colored logarithmic scatterplot of the first 2^16 terms (the color denotes the parity of n: blue for even, red for odd)
- Rémy Sigrist, PARI program
- Index entries for sequences related to binary expansion of n
- Index entries for sequences that are permutations of the natural numbers
Programs
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PARI
See Links section.
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Python
from math import gcd from itertools import count, islice def agen(): # generator of terms aset, v, u = {0}, 0, 1; yield 0 for n in count(1): if v&u != 0: w = u + 1 while w in aset or v&w != 0 or w&u != 0: w += 1 aset.add(w); yield w v = u; aset.add(v); yield v while u in aset: u += 1 print(list(islice(agen(), 65))) # Michael S. Branicky, Jun 24 2022
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