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%I #12 Nov 14 2020 01:50:28
%S 0,1,2,4,3,5,6,12,8,18,14,20,7,13,10,19,16,22,9,15,11,21,17,23,24,48,
%T 30,72,54,96,26,50,49,78,74,102,36,73,60,98,97,108,56,84,80,104,103,
%U 114,25,32,31,55,52,79,28,51,42,76,75,100,38,66,62,99,90,110
%N a(n) is the greatest number not yet in the sequence with the same number of digits and the same sum of digits as n in factorial base.
%C This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A338834/b338834.txt">Table of n, a(n) for n = 0..5039</a>
%H Rémy Sigrist, <a href="/A338834/a338834.png">Colored scatterplot of the first 7! terms</a> (where the color is function of A034968(n))
%H Rémy Sigrist, <a href="/A338834/a338834.gp.txt">PARI program for A338834</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A084558(a(n)) = A084558(n).
%F A034968(a(n)) = A034968(n).
%e For n = 26:
%e - the numbers with 4 digits and sum of digits 2 in factorial base are: 25 ("1001"), 26 ("1010"), 30 ("1100") and 48 ("2000"),
%e - so a(25) = 40,
%e a(26) = 30,
%e a(30) = 26,
%e a(40) = 25.
%o (PARI) See Links section.
%Y Cf. A034968, A084558, A337598, A338829 (decimal analog), A338835 (primorial base analog).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Nov 11 2020
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