A288538 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, n * a(n) does not contain the digit 1 in decimal base.

2, 1, 3, 5, 4, 6, 7, 8, 10, 9, 19, 17, 16, 18, 15, 13, 12, 14, 11, 20, 22, 21, 23, 24, 25, 26, 27, 28, 30, 29, 32, 31, 62, 59, 58, 57, 55, 54, 52, 50, 49, 53, 48, 46, 45, 44, 47, 43, 41, 40, 56, 39, 42, 38, 37, 51, 36, 35, 34, 60, 63, 33, 61, 64, 65, 66, 67

Offset: 1

Author

Rémy Sigrist, Jun 24 2017

Keywords

• nonn
• base

Comments

This sequence is a permutation of the natural numbers; for any n > 0, there are infinitely many values v such that n * v does not contain the digit 1 in decimal base (for example: 2 * A004290(n) / n * 10^k for k = 0, 1, 2,...), hence n will eventually be chosen.

This sequence is self-inverse.

If n is a fixed point, then n^2 belongs to A052383.

The first fixed points are: 3, 6, 7, 8, 15, 20, 23, 24, 25, 26, 27, 28, 45, 47, 60, 64, 65, 66, 67, 68, 75, 76, 77, 78, ...

Examples

			The first terms, alongside n * a(n), are:
n       a(n)    n * a(n)
--      ----    --------
1       2       2
2       1       2
3       3       9
4       5       20
5       4       20
6       6       36
7       7       49
8       8       64
9       10      90
10      9       90
11      19      209
12      17      204
13      16      208
14      18      252
15      15      225
16      13      208
17      12      204
18      14      252
19      11      209
20      20      400
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A288538
• Index entries for sequences that are permutations of the natural numbers
• Rémy Sigrist, Logarithmic scatterplot of the first 10000 terms of n * a(n)

Crossrefs

Cf. A004290, A052383.