A288798 Lexicographically earliest sequence of distinct positive terms such that the absolute difference of two consecutive terms has at least 5 distinct prime factors.

1, 2311, 4621, 331, 2641, 4951, 121, 2431, 4741, 451, 2761, 31, 2341, 4651, 361, 2671, 4981, 151, 2461, 4771, 481, 2791, 61, 2371, 4681, 391, 2701, 5011, 181, 2491, 4801, 511, 2821, 91, 2401, 4711, 421, 2731, 5041, 211, 2521, 4831, 541, 2851, 5161, 871, 3181

Offset

1,2

Comments

Conjecturally: this sequence is a permutation of the natural numbers, and a(n) ~ n.

This sequence is related to A280659: here we consider the absolute difference, there the sum, of consecutive terms.

Links

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

Rémy Sigrist, PARI program for A288798

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       2311    2, 3, 5, 7, 11
3       4621    2, 3, 5,    11, 13
4       331     2, 3, 5, 7, 11
5       2641    2, 3, 5, 7, 11
6       4951    2, 3, 5, 7,         23
7       121     2, 3, 5, 7, 11
8       2431    2, 3, 5, 7, 11
9       4741    2, 3, 5,    11, 13
10      451     2, 3, 5, 7, 11
11      2761    2, 3, 5, 7,     13
12      31      2, 3, 5, 7, 11
13      2341    2, 3, 5, 7, 11
14      4651    2, 3, 5,    11, 13
15      361     2, 3, 5, 7, 11
16      2671    2, 3, 5, 7, 11
17      4981    2, 3, 5, 7,         23
18      151     2, 3, 5, 7, 11
19      2461    2, 3, 5, 7, 11
20      4771    2, 3, 5,    11, 13

Crossrefs

Cf. A280659.

Sequence in context: A087978 A261210 A020435 * A035893 A260049 A184025

Adjacent sequences: A288795 A288796 A288797 * A288799 A288800 A288801

Keyword

nonn

Author

Rémy Sigrist, Jun 16 2017

Status

approved