A329850 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, f(n) * f(a(n)) = f(n * a(n)) where f(m) is the product of the digits of m.

1, 2, 3, 10, 19, 20, 30, 40, 50, 4, 60, 70, 18, 46, 80, 90, 100, 13, 5, 6, 64, 61, 28, 72, 102, 104, 62, 23, 41, 7, 110, 42, 120, 103, 106, 105, 109, 107, 130, 8, 29, 32, 140, 150, 108, 14, 160, 170, 180, 9, 190, 200, 201, 202, 83, 205, 210, 148, 204, 11, 22

Offset

1,2

Comments

This sequence is a variant of A329804; both sequences share graphical features.

This sequence is a self-inverse permutation of the positive integers.

Keyword "look" added in view of the scatterplot of 110000 terms. - N. J. A. Sloane, Nov 23 2019

Links

Rémy Sigrist, Table of n, a(n) for n = 1..21000

Rémy Sigrist, Scatterplot of the first 110000 terms

Rémy Sigrist, Scatterplot of (x, y) such that f(x)*f(y) = f(x*y) and x = 1..1000, y = 1..1000

Rémy Sigrist, C program for A329850

Index entries for sequences that are permutations of the natural numbers

Formula

a(a(n)) = n.

Example

The first terms, alongside f(n), f(a(n)) and f(n*a(n)), are:
  n   a(n)  f(n)  f(a(n))  f(n*a(n))
  --  ----  ----  -------  ---------
   1     1     1        1          1
   2     2     2        2          4
   3     3     3        3          9
   4    10     4        0          0
   5    19     5        9         45
   6    20     6        0          0
   7    30     7        0          0
   8    40     8        0          0
   9    50     9        0          0
  10     4     0        4          0
  11    60     1        0          0
  12    70     2        0          0
  13    18     3        8         24
  14    46     4       24         96

Prog

(C) See Links section.

Crossrefs

Cf. A007954, A329804.

Sequence in context: A143045 A156909 A215121 * A175569 A275020 A122822

Adjacent sequences: A329847 A329848 A329849 * A329851 A329852 A329853

Keyword

nonn,base,look

Author

Rémy Sigrist, Nov 22 2019

Status

approved