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 A382269 #7 Mar 21 2025 14:38:47
%S A382269 0,1,3,5,3,3,11,15,15,23,9,15,11,9,9,11,15,15,11,9,9,11,9,9,47,63,63,
%T A382269 83,39,57,59,87,87,119,57,87,35,57,57,83,39,63,35,57,57,83,33,57,47,
%U A382269 39,39,35,63,57,35,39,39,47,57,63,59,57,57,59,87,87,35,33
%N A382269 The factorial base expansion of a(n) is, when read from right to left, the ordinal transform of that of n.
%C A382269 We ignore nonleading zeros in factorial base expansions.
%C A382269 All terms belong to A382262.
%H A382269 Rémy Sigrist, <a href="/A382269/b382269.txt">Table of n, a(n) for n = 0..5039</a>
%H A382269 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e A382269 The first terms, in decimal and in factorial base, are:
%e A382269 n a(n) fact(n) fact(a(n))
%e A382269 -- ---- ------- ----------
%e A382269 0 0 0 0
%e A382269 1 1 1 1
%e A382269 2 3 1,0 1,1
%e A382269 3 5 1,1 2,1
%e A382269 4 3 2,0 1,1
%e A382269 5 3 2,1 1,1
%e A382269 6 11 1,0,0 1,2,1
%e A382269 7 15 1,0,1 2,1,1
%e A382269 8 15 1,1,0 2,1,1
%e A382269 9 23 1,1,1 3,2,1
%e A382269 10 9 1,2,0 1,1,1
%e A382269 11 15 1,2,1 2,1,1
%e A382269 12 11 2,0,0 1,2,1
%e A382269 13 9 2,0,1 1,1,1
%e A382269 14 9 2,1,0 1,1,1
%e A382269 15 11 2,1,1 1,2,1
%e A382269 16 15 2,2,0 2,1,1
%o A382269 (PARI) a(n) = { my (v = 0, d, f = [0]); for (r = 2, oo, if (n==0, return (v); ); if (#f < r, f = concat(f, vector(#f)); ); v += f[1+(n % r)]++*(r-1)!; n \= r; ); }
%Y A382269 Cf. A382262.
%K A382269 nonn,base
%O A382269 0,3
%A A382269 _Rémy Sigrist_, Mar 20 2025