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

1,1

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, ...

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)

Example

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

Crossrefs

Cf. A004290, A052383.

Sequence in context: A056943 A258654 A171085 * A256210 A256371 A064429

Adjacent sequences: A288535 A288536 A288537 * A288539 A288540 A288541

Keyword

nonn,base

Author

Rémy Sigrist, Jun 24 2017

Status

approved