A285296 -id:A285296 - cp's OEIS frontend

A285297 Inverse permutation to A285296.

1, 3, 5, 2, 7, 4, 9, 6, 8, 11, 14, 10, 16, 12, 18, 13, 21, 15, 23, 17, 19, 25, 28, 20, 22, 26, 24, 27, 30, 32, 36, 29, 33, 38, 41, 31, 43, 39, 34, 35, 45, 40, 47, 37, 42, 49, 51, 44, 46, 48, 53, 50, 55, 52, 57, 54, 59, 61, 65, 56, 67, 62, 58, 60, 69, 63, 73

Offset: 1

Rémy Sigrist, Apr 16 2017

nonn

			A285296(1) = 1, hence a(1) = 1.
A285296(2) = 4, hence a(4) = 2.
A285296(3) = 2, hence a(2) = 3.
A285296(4) = 6, hence a(6) = 4.
A285296(5) = 3, hence a(3) = 5.
A285296(6) = 8, hence a(8) = 6.
A285296(7) = 5, hence a(5) = 7.
A285296(8) = 9, hence a(9) = 8.
A285296(9) = 7, hence a(7) = 9.

Rémy Sigrist, Table of n, a(n) for n = 1..2000
Rémy Sigrist, PARI program for A285297
Index entries for sequences that are permutations of the natural numbers

Cf. A285296.

A285299 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^3 for some prime p.

Original entry on oeis.org

1, 8, 2, 4, 6, 9, 3, 16, 5, 24, 7, 27, 10, 12, 14, 20, 18, 15, 25, 30, 28, 22, 32, 11, 40, 13, 48, 17, 54, 19, 56, 21, 36, 26, 44, 34, 52, 38, 60, 42, 45, 33, 63, 39, 64, 23, 72, 29, 80, 31, 81, 35, 49, 70, 50, 55, 75, 65, 88, 37, 96, 41, 104, 43, 108, 46, 68

Offset: 1

Rémy Sigrist, Apr 16 2017

nonn

This sequence is a permutation of the natural numbers.

			The first terms, alongside the primes p such that p^3 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       8       2
3       2       2
4       4       2
5       6       3
6       9       3
7       3       2
8       16      2
9       5       2
10      24      2
11      7       3
12      27      3
13      10      2
14      12      2
15      14      2
16      20      2
17      18      3
18      15      5
19      25      5
20      30      2
...
64      43      3
65      108     2, 3
66      46      2
...

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C++ program for A285299
Index entries for sequences that are permutations of the natural numbers

Cf. A285296.

A285386 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^4 for some prime p.

Original entry on oeis.org

1, 16, 2, 8, 4, 12, 20, 24, 6, 27, 3, 32, 5, 48, 7, 64, 9, 18, 36, 28, 40, 10, 56, 14, 72, 22, 80, 11, 81, 13, 96, 15, 54, 21, 108, 30, 88, 26, 104, 34, 112, 17, 128, 19, 144, 23, 160, 25, 50, 75, 100, 44, 52, 60, 68, 76, 84, 92, 116, 120, 38, 136, 42, 135, 33

Offset: 1

Rémy Sigrist, Apr 18 2017

nonn

This sequence is a permutation of the natural numbers.

			The first terms, alongside the primes p such that p^4 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       16      2
3       2       2
4       8       2
5       4       2
6       12      2
7       20      2
8       24      2
9       6       3
10      27      3
11      3       2
12      32      2
13      5       2
14      48      2
15      7       2
16      64      2
17      9       3
18      18      3
19      36      2
20      28      2
...
165     95      2
166     432     2, 3
167     87      3
...

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C++ program for A285386
Rémy Sigrist, Scatterplot of the first 100000 terms
Index entries for sequences that are permutations of the natural numbers

Cf. A285296.

A285417 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^5 for some prime p.

Original entry on oeis.org

1, 32, 2, 16, 4, 8, 12, 24, 20, 40, 28, 48, 6, 64, 3, 81, 9, 27, 18, 54, 36, 56, 44, 72, 52, 80, 10, 96, 5, 128, 7, 160, 11, 192, 13, 224, 14, 112, 22, 144, 26, 176, 30, 162, 15, 243, 17, 256, 19, 288, 21, 320, 23, 352, 25, 125, 50, 208, 34, 240, 38, 272, 42

Offset: 1

Rémy Sigrist, Apr 18 2017

nonn

This sequence is a permutation of the natural numbers.

			The first terms, alongside the primes p such that p^5 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       32      2
3       2       2
4       16      2
5       4       2
6       8       2
7       12      2
8       24      2
9       20      2
10      40      2
11      28      2
12      48      2
13      6       2
14      64      2
15      3       3
16      81      3
17      9       3
18      27      3
19      18      3
20      54      3
...
1476    7744    2
1477    811     2, 3
1478    7776    2, 3
1479    813     3
...

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C++ program for A285417
Rémy Sigrist, Scatterplot of the first 150000 terms
Index entries for sequences that are permutations of the natural numbers

Cf. A285296.

A285575 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p.

Original entry on oeis.org

1, 36, 2, 18, 4, 9, 8, 25, 12, 3, 24, 6, 30, 10, 20, 5, 40, 15, 45, 16, 27, 28, 7, 56, 14, 42, 21, 48, 33, 44, 11, 72, 13, 52, 26, 50, 22, 54, 32, 49, 60, 35, 63, 64, 75, 39, 78, 66, 84, 51, 68, 17, 100, 19, 76, 38, 90, 34, 98, 46, 92, 23, 108, 29, 116, 58

Offset: 1

Rémy Sigrist, Apr 22 2017

The sequence can always be extended with a multiple of 36; after a multiple of 36, we can extend the sequence with the least unused number; as there are infinitely many multiples of 36, this sequence is a permutation of the natural numbers (with inverse A285576).
For any k>=0, let c_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms is divisible by p^2 for at least k distinct primes p; in particular we have:
- c_0 = A000027 (the natural numbers),
- c_1 = A285296,
- c_2 = a (this sequence).
For any k>=0, c_k is a permutation of the natural numbers.

			The first terms, alongside the primes p such that p^2 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    ----
1       1       2, 3
2       36      2, 3
3       2       2, 3
4       18      2, 3
5       4       2, 3
6       9       2, 3
7       8       2,    5
8       25      2,    5
9       12      2, 3
10      3       2, 3
11      24      2, 3
12      6       2, 3
13      30      2,    5
14      10      2,    5
15      20      2,    5
16      5       2,    5
17      40      2,    5
18      15         3, 5
19      45      2, 3
20      16      2, 3
...
115     160     2,    5
116     115     2, 3, 5
117     180     2, 3
...

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A285575
Index entries for sequences that are permutations of the natural numbers

Cf. A285296, A285576 (inverse).

cp's OEIS Frontend

A285297 Inverse permutation to A285296.

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A285299 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^3 for some prime p.

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A285386 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^4 for some prime p.

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A285417 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^5 for some prime p.

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A285575 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p.

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