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A342117 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the primorial base representations of n and of a(n) are the same.

%I A342117 #11 Mar 01 2021 02:12:45
%S A342117 0,1,5,3,4,2,27,24,21,9,29,18,17,28,26,16,15,12,11,25,23,8,22,20,7,19,
%T A342117 14,6,13,10,189,147,144,180,207,204,111,159,150,39,201,129,198,197,
%U A342117 196,120,195,108,192,191,188,99,209,187,186,184,183,90,208,182,77
%N A342117 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the primorial base representations of n and of a(n) are the same.
%C A342117 This sequence is a self-inverse permutation of the nonnegative integers.
%H A342117 Rémy Sigrist, <a href="/A342117/b342117.txt">Table of n, a(n) for n = 0..2309</a>
%H A342117 Rémy Sigrist, <a href="/A342117/a342117_1.png">Colored scatterplot of the first 2*3*5*7*11*13 terms</a> (where the color is function of the multiset of frequencies of n)
%H A342117 Rémy Sigrist, <a href="/A342117/a342117.gp.txt">PARI program for A342117</a>
%H A342117 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A342117 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A342117 a(n) < A002110(k) for any n < A002110(k).
%e A342117 The first terms, in decimal and in primorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
%e A342117   n   a(n)  prim(n)  prim(a(n))  freq(n)
%e A342117   --  ----  -------  ----------  ------------
%e A342117    0     0        0           0  ()
%e A342117    1     1        1           1  (1)
%e A342117    2     5       10          21  (1, 1)
%e A342117    3     3       11          11  (2)
%e A342117    4     4       20          20  (1, 1)
%e A342117    5     2       21          10  (1, 1)
%e A342117    6    27      100         411  (1, 2)
%e A342117    7    24      101         400  (1, 2)
%e A342117    8    21      110         311  (1, 2)
%e A342117    9     9      111         111  (3)
%e A342117   10    29      120         421  (1, 1, 1)
%e A342117   11    18      121         300  (1, 2)
%e A342117   12    17      200         221  (1, 2)
%o A342117 (PARI) See Links section.
%Y A342117 See A342102 for similar sequences.
%Y A342117 Cf. A002110, A235168.
%K A342117 nonn,base
%O A342117 0,3
%A A342117 _Rémy Sigrist_, Feb 28 2021