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A333658 a(n) is the greatest number m not yet in the sequence such that the primorial base expansions of n and of m have the same digits (up to order but with multiplicity).

%I A333658 #20 Sep 08 2020 15:17:57
%S A333658 0,1,2,3,4,5,6,8,7,9,14,15,12,13,10,11,16,17,18,20,19,21,22,23,24,26,
%T A333658 25,27,28,29,30,36,32,38,66,68,31,37,33,39,67,69,62,63,44,45,74,75,96,
%U A333658 98,97,99,104,105,126,128,127,129,134,135,60,61,42,43,72,73
%N A333658 a(n) is the greatest number m not yet in the sequence such that the primorial base expansions of n and of m have the same digits (up to order but with multiplicity).
%C A333658 Leading 0's are ignored.
%C A333658 This sequence is a permutation of the nonnegative integers, which preserves the number of digits (A235224) and the sum of digits (A276150) in primorial base.
%H A333658 Rémy Sigrist, <a href="/A333658/b333658.txt">Table of n, a(n) for n = 0..30029</a>
%H A333658 Rémy Sigrist, <a href="/A333658/a333658.png">Scatterplot of the first 2*3*5*7*11*13*17 terms</a>
%H A333658 Rémy Sigrist, <a href="/A333658/a333658.gp.txt">PARI program for A333658</a>
%H A333658 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A333658 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A333658 a(A002110(n)) = A002110(n) for any n >= 0.
%e A333658 For n = 42:
%e A333658 - the primorial base representation of 42 is "1200",
%e A333658 - there are five numbers m with the same multiset of digits:
%e A333658     m   prim(m)
%e A333658     --  -------
%e A333658     34  "1020"
%e A333658     42  "1200"
%e A333658     61  "2001"
%e A333658     62  "2010"
%e A333658     66  "2100"
%e A333658 - so a(34) = 66,
%e A333658      a(42) = 62,
%e A333658      a(61) = 61,
%e A333658      a(62) = 42,
%e A333658      a(66) = 34.
%o A333658 (PARI) See Links section.
%Y A333658 See A333659 and A337598 for similar sequences.
%Y A333658 Cf. A002110, A235224, A276150.
%K A333658 nonn,look,base
%O A333658 0,3
%A A333658 _Rémy Sigrist_, Sep 02 2020