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A319023
Let S be the sequence generated by these rules: 1 is in S, and if k is in S, then A057168(k) and A319021(k) are in S, and duplicates are deleted as they occur; a(n) is the n-th term of S.
2
1, 2, 3, 4, 5, 9, 8, 6, 7, 10, 27, 16, 14, 11, 12, 29, 81, 32, 20, 19, 13, 17, 18, 30, 31, 82, 243, 64, 34, 24, 22, 21, 15, 23, 28, 39, 36, 47, 33, 84, 245, 729, 128, 66, 38, 25, 35, 43, 45, 40, 54, 55, 49, 37, 88, 90, 246, 247, 730, 2187, 256, 130, 68, 72, 41
OFFSET
1,2
COMMENTS
This sequence is a permutation of the natural numbers (with inverse A319024):
- this sequence is injective,
- this sequence is surjective: by contradiction:
- let m be the least integer missing from the sequence,
- as a(1) = 1, we have m > 1,
- also, m belongs to A000225 and to A062318,
- however the only positive integer belonging to both sequences is 1,
- hence a contradiction, QED.
EXAMPLE
The first terms, alongside b(n) = A057168(a(n)) and t(n) = A319021(a(n)), are:
n a(n) b(n) t(n)
-- ---- ---- ----
1 1 2 3
2 2 4 4
3 3 5 9
4 4 8 6
5 5 6 7
6 9 10 27
7 8 16 14
8 6 9 10
9 7 11 11
10 10 12 12
11 27 29 81
12 16 32 20
13 14 19 16
14 11 13 13
15 12 17 18
16 29 30 31
17 81 82 243
18 32 64 34
19 20 24 22
20 19 21 21
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A092975 A164340 A046021 * A335910 A362814 A371152
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Sep 08 2018
STATUS
approved