A288171 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+3) has at least 5 distinct prime factors.

1, 2, 3, 2310, 1155, 770, 4, 6, 9, 1365, 385, 910, 8, 12, 11, 1785, 455, 210, 10, 18, 13, 231, 595, 330, 20, 22, 7, 273, 105, 390, 30, 26, 14, 77, 165, 195, 60, 28, 34, 91, 255, 285, 66, 38, 42, 35, 315, 55, 78, 44, 84, 70, 345, 65, 33, 52, 102, 130, 357, 95

Offset

1,2

Comments

This sequence is a permutation of the natural numbers, with inverse A288800.

See also A288164 for similar sequences.

Conjecturally, a(n) ~ n.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Rémy Sigrist, C++ program for A288171

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the primes p dividing a(n)*a(n+3), are:
n       a(n)    p
--      ----    --------------
1       1       2, 3, 5, 7, 11
2       2       2, 3, 5, 7, 11
3       3       2, 3, 5, 7, 11
4       2310    2, 3, 5, 7, 11
5       1155    2, 3, 5, 7, 11
6       770     2, 3, 5, 7, 11
7       4       2, 3, 5, 7,     13
8       6       2, 3, 5, 7, 11
9       9       2, 3, 5, 7,     13
10      1365    2, 3, 5, 7,     13
11      385     2, 3, 5, 7, 11
12      910     2,    5, 7, 11, 13
13      8       2, 3, 5, 7,         17
14      12      2, 3, 5, 7,     13
15      11      2, 3, 5, 7, 11
16      1785    2, 3, 5, 7,         17
17      455     2, 3, 5, 7,     13
18      210     2, 3, 5, 7,     13
19      10      2, 3, 5, 7, 11
20      18      2, 3, 5, 7,         17

Crossrefs

Cf. A288164, A288800 (inverse).

Sequence in context: A323518 A004909 A266585 * A137321 A066848 A324310

Adjacent sequences: A288168 A288169 A288170 * A288172 A288173 A288174

Keyword

nonn,look

Author

Rémy Sigrist, Jun 16 2017

Status

approved