A288164 -id:A288164 - cp's OEIS frontend

A288799 Inverse permutation to A288164.

1, 2, 5, 6, 57, 9, 45, 10, 222, 14, 41, 13, 49, 29, 61, 954, 53, 17, 178, 18, 54, 21, 182, 226, 198, 25, 426, 33, 186, 22, 190, 958, 50, 134, 32, 230, 194, 37, 58, 146, 202, 38, 206, 138, 65, 150, 210, 234, 214, 154, 62, 142, 218, 238, 36, 162, 66, 158, 350

Offset: 1

Rémy Sigrist, Jun 16 2017

			A288164(1) = 1, hence a(1) = 1.
A288164(2) = 2, hence a(2) = 2.
A288164(3) = 2310, hence a(2310) = 3.
A288164(4) = 1155, hence a(1155) = 4.
A288164(5) = 3, hence a(3) = 5.
A288164(6) = 4, hence a(4) = 6.
A288164(7) = 770, hence a(770) = 7.
A288164(8) = 1365, hence a(1365) = 8.
A288164(9) = 6, hence a(6) = 9.
A288164(10) = 8, hence a(8) = 10.

Cf. A288164.

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.

Original entry on oeis.org

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

Rémy Sigrist, Jun 16 2017

This sequence is a permutation of the natural numbers, with inverse A288800.
See also A288164 for similar sequences.
Conjecturally, a(n) ~ n.

			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

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

Cf. A288164, A288800 (inverse).

cp's OEIS Frontend

A288799 Inverse permutation to A288164.

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