A329804 -id:A329804 - cp's OEIS frontend

A330326 a(1)=1; thereafter a(n) = b(n)*b(n-1), where b = A329804.

1, 2, 6, 30, 40, 64, 320, 100, 95, 570, 180, 126, 840, 280, 350, 400, 480, 540, 630, 770, 880, 960, 1080, 1170, 234, 684, 3800, 1400, 644, 4830, 2310, 1342, 2196, 3708, 3502, 3604, 1590, 1395, 10044, 2700, 2550, 3570, 1435, 1189, 3016, 2704, 2860, 1870

Offset: 1

N. J. A. Sloane, Dec 12 2019

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A329804, A330327.

A330327 a(1)=1; thereafter a(n) = (product of digits of b(n))*(product of digits of b(n-1)), where b = A329804.

Original entry on oeis.org

1, 2, 6, 0, 0, 24, 0, 0, 45, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 192, 0, 0, 96, 0, 0, 24, 108, 0, 0, 0, 0, 135, 0, 0, 0, 0, 60, 72, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 112, 0, 0, 0, 0, 168, 36, 0, 0, 48, 0, 0, 0, 0, 0, 0, 672, 0, 0, 160, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600

Offset: 1

N. J. A. Sloane, Dec 12 2019

By definition, a(n) is also equal to the product of the digits of A330326(n).

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A329804, A330326.

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.

Original entry on oeis.org

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

Rémy Sigrist, Nov 22 2019

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

			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

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

Cf. A007954, A329804.

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a(a(n)) = n.

cp's OEIS Frontend

A330326 a(1)=1; thereafter a(n) = b(n)*b(n-1), where b = A329804.

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A330327 a(1)=1; thereafter a(n) = (product of digits of b(n))*(product of digits of b(n-1)), where b = A329804.

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Author

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Links

Crossrefs

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.

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