A288171 -id:A288171 - cp's OEIS frontend

A288800 Inverse permutation to A288171.

1, 2, 3, 7, 80, 8, 27, 13, 9, 19, 15, 14, 21, 33, 79, 1028, 74, 20, 86, 25, 61, 26, 92, 248, 122, 32, 452, 38, 98, 31, 104, 1034, 55, 39, 46, 254, 110, 44, 67, 62, 116, 45, 128, 50, 85, 68, 134, 260, 146, 158, 73, 56, 140, 266, 48, 152, 91, 164, 386, 37, 392

Offset: 1

Rémy Sigrist, Jun 16 2017

			A288171(1) = 1, hence a(1) = 1.
A288171(2) = 2, hence a(2) = 2.
A288171(3) = 3, hence a(3) = 3.
A288171(4) = 2310, hence a(2310) = 4.
A288171(5) = 1155, hence a(1155) = 5.
A288171(6) = 770, hence a(770) = 6.
A288171(7) = 4, hence a(4) = 7.
A288171(8) = 6, hence a(6) = 8.
A288171(9) = 9, hence a(9) = 9.
A288171(10) = 1365, hence a(1365) = 10.

Cf. A288171.

A288164 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+2) has at least 5 distinct prime factors.

Original entry on oeis.org

1, 2, 2310, 1155, 3, 4, 770, 1365, 6, 8, 385, 1785, 12, 10, 455, 231, 18, 20, 595, 273, 22, 30, 105, 77, 26, 60, 165, 91, 14, 66, 195, 35, 28, 78, 255, 55, 38, 42, 210, 65, 11, 84, 390, 85, 7, 114, 330, 70, 13, 33, 420, 130, 17, 21, 462, 110, 5, 39, 546, 140

Offset: 1

Rémy Sigrist, Jun 16 2017

This sequence is a permutation of the natural numbers, with inverse A288799.
Conjecturally, a(n) ~ n.
For k >= 0, let f_k be the lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+k) has at least 5 distinct prime factors.
In particular, we have:
- f_0 = the numbers with at least 5 distinct prime factors,
- f_1 = A285487,
- f_2 = a (this sequence),
- f_3 = A288171.
If k > 0, then:
- f_k is a permutation of the natural numbers,
- f_k(i) = i for any i <= k,
- f_k(k+1) = A002110(5),
- conjecturally, f_k(n) ~ n.

			The first terms, alongside the primes p dividing a(n)*a(n+2), are:
n       a(n)    p
--      ----    --------------
1       1       2, 3, 5, 7, 11
2       2       2, 3, 5, 7, 11
3       2310    2, 3, 5, 7, 11
4       1155    2, 3, 5, 7, 11
5       3       2, 3, 5, 7, 11
6       4       2, 3, 5, 7,     13
7       770     2, 3, 5, 7, 11
8       1365    2, 3, 5, 7,     13
9       6       2, 3, 5, 7, 11
10      8       2, 3, 5, 7,         17
11      385     2, 3, 5, 7, 11
12      1785    2, 3, 5, 7,         17
13      12      2, 3, 5, 7,     13
14      10      2, 3, 5, 7, 11
15      455     2, 3, 5, 7,     13
16      231     2, 3, 5, 7, 11
17      18      2, 3, 5, 7,         17
18      20      2, 3, 5, 7,     13
19      595     2,    5, 7, 11,     17
20      273     2, 3, 5, 7,     13
21      22      2, 3, 5, 7, 11
22      30      2, 3, 5, 7, 11
23      105     2, 3, 5, 7,     13

Rémy Sigrist, Table of n, a(n) for n = 1..25000
Rémy Sigrist, C++ program for A288164
Index entries for sequences that are permutations of the natural numbers

Cf. A002110, A285487, A288171, A288799 (inverse).

cp's OEIS Frontend

A288800 Inverse permutation to A288171.

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