

A343476


Numbers k whose representations in factorial base include each of the digits from 0 to d1 exactly once, where d = A084558(k) is the number of digits of k in factorial base.


2



0, 2, 10, 13, 14, 46, 67, 68, 77, 82, 85, 86, 238, 355, 356, 461, 466, 469, 470, 503, 526, 547, 548, 557, 562, 565, 566, 1438, 2155, 2156, 2861, 2866, 2869, 2870, 3503, 3526, 3547, 3548, 3557, 3562, 3565, 3566, 3719, 3838, 3955, 3956, 4061, 4066, 4069, 4070, 4103
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OFFSET

1,2


COMMENTS

The number of terms with k > 1 digits in factorial base is 2^(k1)  1 = A000225(k1).
The number of terms below k!, for k >= 1, is 2^(k1)  (k1) = A000325(k1).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000
Wikipedia, Factorial number system.


EXAMPLE

2 is a term since its factorial base representation is {1, 0}.
10, 13 and 14 are terms since their factorial base representations are {1, 2, 0}, {2, 0, 1} and {2, 1, 0}, respectively.


MATHEMATICA

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]


CROSSREFS

A065355 is a subsequence.
Cf. A000225, A000325, A007623, A084558, A343477.
Sequence in context: A189079 A045218 A177856 * A343477 A296220 A297835
Adjacent sequences: A343473 A343474 A343475 * A343477 A343478 A343479


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Apr 16 2021


STATUS

approved



