A343476 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.
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
Offset: 1
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
- Wikipedia, Factorial number system.
Programs
-
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]
Comments