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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.

%I A329850 #14 Nov 23 2019 13:58:06
%S A329850 1,2,3,10,19,20,30,40,50,4,60,70,18,46,80,90,100,13,5,6,64,61,28,72,
%T A329850 102,104,62,23,41,7,110,42,120,103,106,105,109,107,130,8,29,32,140,
%U A329850 150,108,14,160,170,180,9,190,200,201,202,83,205,210,148,204,11,22
%N 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.
%C A329850 This sequence is a variant of A329804; both sequences share graphical features.
%C A329850 This sequence is a self-inverse permutation of the positive integers.
%C A329850 Keyword "look" added in view of the scatterplot of 110000 terms. - _N. J. A. Sloane_, Nov 23 2019
%H A329850 Rémy Sigrist, <a href="/A329850/b329850.txt">Table of n, a(n) for n = 1..21000</a>
%H A329850 Rémy Sigrist, <a href="/A329850/a329850.png">Scatterplot of the first 110000 terms</a>
%H A329850 Rémy Sigrist, <a href="/A329850/a329850_1.png">Scatterplot of (x, y) such that f(x)*f(y) = f(x*y) and x = 1..1000, y = 1..1000</a>
%H A329850 Rémy Sigrist, <a href="/A329850/a329850.txt">C program for A329850</a>
%H A329850 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A329850 a(a(n)) = n.
%e A329850 The first terms, alongside f(n), f(a(n)) and f(n*a(n)), are:
%e A329850   n   a(n)  f(n)  f(a(n))  f(n*a(n))
%e A329850   --  ----  ----  -------  ---------
%e A329850    1     1     1        1          1
%e A329850    2     2     2        2          4
%e A329850    3     3     3        3          9
%e A329850    4    10     4        0          0
%e A329850    5    19     5        9         45
%e A329850    6    20     6        0          0
%e A329850    7    30     7        0          0
%e A329850    8    40     8        0          0
%e A329850    9    50     9        0          0
%e A329850   10     4     0        4          0
%e A329850   11    60     1        0          0
%e A329850   12    70     2        0          0
%e A329850   13    18     3        8         24
%e A329850   14    46     4       24         96
%o A329850 (C) See Links section.
%Y A329850 Cf. A007954, A329804.
%K A329850 nonn,base,look
%O A329850 1,2
%A A329850 _Rémy Sigrist_, Nov 22 2019