A285487 - OEIS

A285487

Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct prime factors.

1, 2310, 2, 1155, 4, 1365, 6, 385, 12, 455, 18, 595, 22, 105, 26, 165, 14, 195, 28, 255, 38, 210, 11, 390, 7, 330, 13, 420, 17, 462, 5, 546, 10, 231, 20, 273, 30, 77, 60, 91, 66, 35, 78, 55, 42, 65, 84, 85, 114, 70, 33, 130, 21, 110, 39, 140, 51, 154, 15, 182

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This sequence can always be extended with a multiple of 2310 = 2*3*5*7*11; after a term that has at least 5 distinct prime factors, we can extend the sequence with the least unused number; as there are infinitely many numbers with at least 5 distinct prime factors, this sequence is a permutation of the natural numbers (with inverse A285488).

Conjecturally, a(n) ~ n.

The first fixed points are: 1, 75, 295, 375, 1205, 1207, 1211, 6017, 19870, 19872, 19874, 19878, 19907, 19909.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..30000

Rémy Sigrist, C++ program for A285487

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The first terms, alongside the primes p dividing a(n)*a(n+1), are:

n a(n) p

-- ---- --------------

1 1 2, 3, 5, 7, 11

2 2310 2, 3, 5, 7, 11