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

Author

Rémy Sigrist, Nov 22 2019

Keywords

• nonn
• base
• look

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

Examples

			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
		

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

Crossrefs

Cf. A007954, A329804.

Programs

C

See Links section.

Formula

a(a(n)) = n.