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A355435
Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple of a(A080079(n-1)).
2
1, 2, 4, 3, 6, 8, 10, 5, 15, 20, 16, 12, 9, 24, 14, 7, 21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11, 33, 66, 88, 54, 84, 112, 100, 75, 60, 80, 64, 72, 90, 96, 140, 63, 35, 70, 120, 45, 108, 128, 160, 105, 55, 110, 104, 78, 39, 52, 26, 13
OFFSET
1,2
COMMENTS
This sequence is a permutation of the positive integers with inverse A355436.
The construction of this sequence is similar to that of A269838.
This sequence can also be seen as an irregular table:
- with row lengths given by A011782,
- with initial row (1),
- given the first k+1 rows (with globally 2^k terms), the next row contains a multiple of a(2^k), followed by a multiple of a(2^k-1), ..., followed by a multiple of a(1).
FORMULA
a(2^n) = prime(n) for any n > 0 (where prime(n) denotes the n-th prime number).
EXAMPLE
As an irregular table, the first rows are:
[1]
[2]
[4, 3]
[6, 8, 10, 5]
[15, 20, 16, 12, 9, 24, 14, 7]
[21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11]
.
The first terms are:
n a(n) A080079(n-1) a(A080079(n-1))
-- ---- ------------ ---------------
1 1 N/A N/A
2 2 1 1
3 4 2 2
4 3 1 1
5 6 4 3
6 8 3 4
7 10 2 2
8 5 1 1
9 15 8 5
10 20 7 10
11 16 6 8
12 12 5 6
13 9 4 3
14 24 3 4
15 14 2 2
16 7 1 1
PROG
(PARI) See Links section.
CROSSREFS
Cf. A011782, A080079, A269838, A355436 (inverse).
Sequence in context: A297403 A120241 A352714 * A155487 A356430 A128555
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Jul 02 2022
STATUS
approved