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

Author

Rémy Sigrist, Jun 16 2017

Keywords

• nonn
• look

Comments

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

See also A288164 for similar sequences.

Conjecturally, a(n) ~ n.

Examples

			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
		

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

Crossrefs

Cf. A288164, A288800 (inverse).