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A360959
Order the nonnegative integers by increasing number of digits in base 2, then by decreasing number of digits in base 3, then by increasing number of digits in base 4, etc.
3
0, 1, 3, 2, 5, 7, 6, 4, 9, 11, 13, 15, 14, 12, 10, 8, 27, 29, 31, 30, 28, 25, 26, 17, 19, 21, 23, 24, 22, 20, 18, 16, 33, 35, 34, 32, 49, 51, 53, 55, 57, 59, 61, 63, 62, 60, 58, 56, 54, 52, 50, 37, 39, 41, 43, 45, 47, 48, 46, 44, 42, 40, 38, 36, 125, 127, 126
OFFSET
0,3
COMMENTS
We ignore leading zeros.
This sequence is a permutation of the nonnegative integers with inverse A360960.
The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360964(x, y): even implies x appears after y, odd implies x appears before y.
FORMULA
a(n) < 2^k for any n < 2^k.
EXAMPLE
The first terms, alongside their number of digits in small bases, are:
n a(n) w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13 w14 w15
-- ---- -- -- -- -- -- -- -- -- --- --- --- --- --- ---
0 0 0
1 1 1
2 3 2 2
3 2 2 1
4 5 3 2 2 2 1
5 7 3 2 2 2 2 2
6 6 3 2 2 2 2 1
7 4 3 2 2 1
8 9 4 3 2 2 2 2 2 2 1
9 11 4 3 2 2 2 2 2 2 2 2 1
10 13 4 3 2 2 2 2 2 2 2 2 2 2 1
11 15 4 3 2 2 2 2 2 2 2 2 2 2 2 2
12 14 4 3 2 2 2 2 2 2 2 2 2 2 2 1
13 12 4 3 2 2 2 2 2 2 2 2 2 1
14 10 4 3 2 2 2 2 2 2 2 1
15 8 4 2
PROG
(PARI) See Links section.
CROSSREFS
See A360982 for a similar sequence.
Cf. A360960 (inverse), A360964.
Sequence in context: A118320 A108918 A316472 * A341910 A341915 A371975
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 27 2023
STATUS
approved