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A367288
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Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(n-1) and a(n) are congruent modulo n, and the least value not yet in the sequence appears as soon as possible.
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5
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0, 1, 5, 2, 18, 3, 39, 4, 60, 6, 106, 7, 151, 8, 204, 9, 265, 10, 334, 11, 411, 12, 496, 13, 589, 14, 690, 15, 799, 16, 916, 17, 1009, 19, 1175, 20, 1316, 21, 1465, 22, 1622, 23, 1787, 24, 1960, 25, 2141, 26, 2330, 27, 2527, 28, 2732, 29, 2945, 30, 3166, 31
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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To build the sequence:
- we start with a(0) = 0, and repeatedly:
- let a(n) be the last known term and v the least value not yet in the sequence,
- if a(n) and v are congruent modulo n+1 then a(n+1) = v,
- otherwise a(n+2) = v and a(n+1) is chosen as small as possible in such a way as to satisfy the required congruences (this is always possible as n+1 and n+2 are coprime).
This construction is similar to that of A352713.
This sequence is a variant of A125717 and, by design, is guaranteed to be a permutation of the nonnegative integers (with inverse A367289).
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LINKS
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EXAMPLE
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The first terms are:
n a(n) a(n-1) mod n a(n) mod n
-- ---- ------------ ----------
0 0 N/A N/A
1 1 0 0
2 5 1 1
3 2 2 2
4 18 2 2
5 3 3 3
6 39 3 3
7 4 4 4
8 60 4 4
9 6 6 6
10 106 6 6
11 7 7 7
12 151 7 7
13 8 8 8
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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