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A299441
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Lexicographically earliest sequence of distinct positive terms such that, for any n > 1, if prime(k) is the least prime factor of a(n) then k divides a(n+1) (where prime(k) denotes the k-th prime).
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4
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 12, 13, 18, 14, 16, 17, 21, 20, 19, 24, 22, 23, 27, 26, 25, 30, 28, 29, 40, 31, 33, 32, 34, 35, 36, 37, 48, 38, 39, 42, 41, 52, 43, 56, 44, 45, 46, 47, 60, 49, 64, 50, 51, 54, 53, 80, 55, 57, 58, 59, 68, 61, 72, 62, 63
(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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In other words, for any n > 1, A055396(a(n)) divides a(n+1).
This sequence has similarities with A285039 (especially visually).
See also A299442 for the variant involving greatest prime factors.
This sequence is a permutation of the natural numbers, with inverse A299703:
- for any n > 1, if a(n) is odd, then lpf(a(n+1)) < lpf(a(n)), and a(n+k) will be even for some k > 0 (where lpf = A020639),
- hence we have infinitely many even terms,
- and as after an even term, we can choose the least positive number not yet in the sequence, eventually every positive number will appear.
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LINKS
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EXAMPLE
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The first terms, alongside A055396(a(n)), are:
-- ---- -------------
1 1 0
2 2 1
3 3 2
4 4 1
5 5 3
6 6 1
7 7 4
8 8 1
9 9 2
10 10 1
11 11 5
12 15 2
13 12 1
14 13 6
15 18 1
16 14 1
17 16 1
18 17 7
19 21 2
20 20 1
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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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