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%I #11 Mar 01 2021 02:12:45
%S 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 14,6,13,10,189,147,144,180,207,204,111,159,150,39,201,129,198,197,
%U 196,120,195,108,192,191,188,99,209,187,186,184,183,90,208,182,77
%N 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 This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A342117/b342117.txt">Table of n, a(n) for n = 0..2309</a>
%H 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 Rémy Sigrist, <a href="/A342117/a342117.gp.txt">PARI program for A342117</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) < A002110(k) for any n < A002110(k).
%e The first terms, in decimal and in primorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
%e n a(n) prim(n) prim(a(n)) freq(n)
%e -- ---- ------- ---------- ------------
%e 0 0 0 0 ()
%e 1 1 1 1 (1)
%e 2 5 10 21 (1, 1)
%e 3 3 11 11 (2)
%e 4 4 20 20 (1, 1)
%e 5 2 21 10 (1, 1)
%e 6 27 100 411 (1, 2)
%e 7 24 101 400 (1, 2)
%e 8 21 110 311 (1, 2)
%e 9 9 111 111 (3)
%e 10 29 120 421 (1, 1, 1)
%e 11 18 121 300 (1, 2)
%e 12 17 200 221 (1, 2)
%o (PARI) See Links section.
%Y See A342102 for similar sequences.
%Y Cf. A002110, A235168.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Feb 28 2021
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