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A343506 Numbers k such that the largest digit in the factorial base expansion of 1/k is 1.

%I A343506 #13 Apr 20 2021 10:09:57
%S A343506 1,2,6,20,24,120,630,720,4480,5040,36288,40320,362880,3326400,3628800,
%T A343506 39916800
%N A343506 Numbers k such that the largest digit in the factorial base expansion of 1/k is 1.
%C A343506 Equivalently these are the numbers k such that A299020(k) = 1 or A343505(k) = 1.
%C A343506 This sequence is infinite as it contains:
%C A343506 - the factorial numbers (A000142),
%C A343506 - 1/(1/A060462(k)! + 1/(A060462(k)-1)!) for k > 2,
%C A343506 - 1/(1/A120416(k)! + 1/(A120416(k)-1)! + 1/(A120416(k)-2)!) for k > 0.
%H A343506 Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system#Fractional_values">Factorial number system (Fractional values)</a>
%H A343506 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e A343506 The first terms, alongside the factorial base expansion of their inverse, are:
%e A343506   n   a(n)     1/a(n) in factorial base
%e A343506   --  -------  ------------------------
%e A343506    1        1  1
%e A343506    2        2  0.1
%e A343506    3        6  0.0 1
%e A343506    4       20  0.0 0 1 1
%e A343506    5       24  0.0 0 1
%e A343506    6      120  0.0 0 0 1
%e A343506    7      630  0.0 0 0 0 1 1
%e A343506    8      720  0.0 0 0 0 1
%e A343506    9     4480  0.0 0 0 0 0 1 1
%e A343506   10     5040  0.0 0 0 0 0 1
%e A343506   11    36288  0.0 0 0 0 0 0 1 1
%e A343506   12    40320  0.0 0 0 0 0 0 1
%e A343506   13   362880  0.0 0 0 0 0 0 0 1
%e A343506   14  3326400  0.0 0 0 0 0 0 0 0 1 1
%e A343506   15  3628800  0.0 0 0 0 0 0 0 0 1
%o A343506 (PARI) is(n) = my (f=1/n); for (r=2, oo, if (f==0, return (1), floor(f)>1, return (0), f=frac(f)*r))
%Y A343506 Cf. A000142, A060462, A120416, A294168, A299020, A343505.
%Y A343506 Cf. A333402 (decimal).
%K A343506 nonn,base,more
%O A343506 1,2
%A A343506 _Rémy Sigrist_, Apr 17 2021