This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382313 #6 Mar 22 2025 08:44:35
%S A382313 0,1,5,3,5,5,15,11,17,9,23,11,15,23,23,15,17,17,15,23,23,15,23,23,57,
%T A382313 41,59,39,83,47,63,35,65,33,95,35,87,47,71,39,89,41,87,47,71,39,119,
%U A382313 47,57,89,83,87,59,71,87,83,89,57,71,59,63,95,95,63,65,65,87
%N A382313 The factorial base expansion of a(n) corresponds to the restricted growth sequence of that of n (when read from right to left).
%C A382313 We ignore nonleading zeros in factorial base expansions.
%C A382313 All terms belong to A120696.
%H A382313 Rémy Sigrist, <a href="/A382313/b382313.txt">Table of n, a(n) for n = 0..5039</a>
%H A382313 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A382313 a(a(n)) = a(n).
%e A382313 The first terms, in decimal and in factorial base, are:
%e A382313 n a(n) fact(n) fact(a(n))
%e A382313 -- ---- ------- ----------
%e A382313 0 0 0 0
%e A382313 1 1 1 1
%e A382313 2 5 10 21
%e A382313 3 3 11 11
%e A382313 4 5 20 21
%e A382313 5 5 21 21
%e A382313 6 15 100 211
%e A382313 7 11 101 121
%e A382313 8 17 110 221
%e A382313 9 9 111 111
%e A382313 10 23 120 321
%e A382313 11 11 121 121
%e A382313 12 15 200 211
%e A382313 13 23 201 321
%e A382313 14 23 210 321
%e A382313 15 15 211 211
%o A382313 (PARI) a(n) = { my (v = 0, m = Map(), u = 0, d, c); for (r = 2, oo, if (n==0, return (v), d = n%r; n \= r; if (!mapisdefined(m, d, &c), mapput(m, d, c=u++);); v += c*(r-1)!;);); }
%Y A382313 See A382269 for a similar sequence.
%Y A382313 Cf. A120696.
%K A382313 nonn,base,easy
%O A382313 0,3
%A A382313 _Rémy Sigrist_, Mar 21 2025