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A382262 Nonnegative numbers whose factorial base expansion, when read from right to left, corresponds to the ordinal transform of some finite sequence, with offset 0.

%I A382262 #10 Mar 21 2025 14:39:18
%S A382262 0,1,3,5,9,11,15,23,33,35,39,47,57,59,63,83,87,119,153,155,159,167,
%T A382262 177,179,183,203,207,239,273,275,279,287,297,323,327,395,399,417,419,
%U A382262 423,527,563,567,719,873,875,879,887,897,899,903,923,927,959,993,995
%N A382262 Nonnegative numbers whose factorial base expansion, when read from right to left, corresponds to the ordinal transform of some finite sequence, with offset 0.
%C A382262 We ignore leading zeros in factorial base expansions.
%C A382262 A subsequence of A120696.
%C A382262 There are A000085(k) terms whose factorial base expansion has k digits.
%H A382262 Rémy Sigrist, <a href="/A382262/b382262.txt">Table of n, a(n) for n = 0..13231</a>
%H A382262 Rémy Sigrist, <a href="/A382262/a382262.gp.txt">PARI program</a>
%H A382262 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e A382262 The first terms, in decimal and in factorial base, are:
%e A382262   n   a(n)  fact(a(n))
%e A382262   --  ----  ----------
%e A382262    0     0  0
%e A382262    1     1  1
%e A382262    2     3  1,1
%e A382262    3     5  2,1
%e A382262    4     9  1,1,1
%e A382262    5    11  1,2,1
%e A382262    6    15  2,1,1
%e A382262    7    23  3,2,1
%e A382262    8    33  1,1,1,1
%e A382262    9    35  1,1,2,1
%e A382262   10    39  1,2,1,1
%e A382262   11    47  1,3,2,1
%e A382262   12    57  2,1,1,1
%e A382262   13    59  2,1,2,1
%e A382262   14    63  2,2,1,1
%e A382262   15    83  3,1,2,1
%e A382262   16    87  3,2,1,1
%e A382262   17   119  4,3,2,1
%e A382262   18   153  1,1,1,1,1
%o A382262 (PARI) \\ See Links section.
%Y A382262 Cf. A000085, A120696, A382263.
%K A382262 nonn,base
%O A382262 0,3
%A A382262 _Rémy Sigrist_, Mar 19 2025