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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 01:55 EDT 2021. Contains 343937 sequences. (Running on oeis4.)