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A367290
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Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n) and a(n+1) are congruent modulo the n-th prime number, and the least value not yet in the sequence appears as soon as possible.
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3
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1, 5, 2, 17, 3, 69, 4, 310, 6, 558, 7, 193, 8, 869, 9, 2077, 10, 1780, 11, 3562, 12, 961, 13, 6155, 14, 2439, 15, 8255, 16, 6120, 18, 12464, 19, 9472, 20, 11195, 21, 4260, 22, 24070, 23, 16133, 24, 18360, 25, 19528, 26, 27456, 27, 25905, 28, 46395, 29, 6054
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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To build the sequence:
- we start with a(1) = 1, 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 the n-th prime number 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 two consecutive prime numbers are coprime).
This sequence is a variant of A364054, and, by design, is guaranteed to be a permutation of the positive integers (with inverse A367291).
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LINKS
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EXAMPLE
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The first terms are:
n a(n) a(n) mod prime(n) a(n+1) mod prime(n)
-- ----- ----------------- -------------------
1 1 1 1
2 5 2 2
3 2 2 2
4 17 3 3
5 3 3 3
6 69 4 4
7 4 4 4
8 310 6 6
9 6 6 6
10 558 7 7
11 7 7 7
12 193 8 8
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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