A285417 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^5 for some prime p.

1, 32, 2, 16, 4, 8, 12, 24, 20, 40, 28, 48, 6, 64, 3, 81, 9, 27, 18, 54, 36, 56, 44, 72, 52, 80, 10, 96, 5, 128, 7, 160, 11, 192, 13, 224, 14, 112, 22, 144, 26, 176, 30, 162, 15, 243, 17, 256, 19, 288, 21, 320, 23, 352, 25, 125, 50, 208, 34, 240, 38, 272, 42

Offset

1,2

Comments

This sequence is a permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C++ program for A285417

Rémy Sigrist, Scatterplot of the first 150000 terms

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the primes p such that p^5 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       32      2
3       2       2
4       16      2
5       4       2
6       8       2
7       12      2
8       24      2
9       20      2
10      40      2
11      28      2
12      48      2
13      6       2
14      64      2
15      3       3
16      81      3
17      9       3
18      27      3
19      18      3
20      54      3
...
1476    7744    2
1477    811     2, 3
1478    7776    2, 3
1479    813     3
...

Crossrefs

Cf. A285296.

Sequence in context: A373777 A221760 A037932 * A303328 A298921 A070631

Adjacent sequences: A285414 A285415 A285416 * A285418 A285419 A285420

Keyword

nonn

Author

Rémy Sigrist, Apr 18 2017

Status

approved