A343476 - OEIS

%I #11 Apr 17 2021 03:58:28

%S 0,2,10,13,14,46,67,68,77,82,85,86,238,355,356,461,466,469,470,503,

%T 526,547,548,557,562,565,566,1438,2155,2156,2861,2866,2869,2870,3503,

%U 3526,3547,3548,3557,3562,3565,3566,3719,3838,3955,3956,4061,4066,4069,4070,4103

%N Numbers k whose representations in factorial base include each of the digits from 0 to d-1 exactly once, where d = A084558(k) is the number of digits of k in factorial base.

%C The number of terms with k > 1 digits in factorial base is 2^(k-1) - 1 = A000225(k-1).

%C The number of terms below k!, for k >= 1, is 2^(k-1) - (k-1) = A000325(k-1).

%H Amiram Eldar, <a href="/A343476/b343476.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>.

%e 2 is a term since its factorial base representation is {1, 0}.

%e 10, 13 and 14 are terms since their factorial base representations are {1, 2, 0}, {2, 0, 1} and {2, 1, 0}, respectively.

%t m = 7; bases = Reverse @ Range[2, m]; max = Times @@ bases; factBase[n_] := IntegerDigits[n, MixedRadix[bases]]; q[n_] := Union[(fd = factBase[n])] == Range[0, Length[fd] - 1]; Select[Range[0, max], q]

%Y A065355 is a subsequence.

%Y Cf. A000225, A000325, A007623, A084558, A343477.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Apr 16 2021