A343477 - OEIS

%I #10 Apr 17 2021 03:58:31

%S 0,2,10,13,14,52,79,80,95,100,103,104,328,352,535,536,559,560,659,688,

%T 715,716,755,760,763,764,863,892,919,920,935,940,943,944,3118,3322,

%U 3478,3502,5425,5426,5629,5630,5785,5786,5809,5810,7109,7318,7525,7526,7925

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

%H Amiram Eldar, <a href="/A343477/b343477.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Mixed_radix#Primorial_number_system">Primorial number system</a>.

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

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

%t m = 6; bases = Reverse @ Prime @ Range[m]; max = Times @@ bases; primBase[n_] := IntegerDigits[n, MixedRadix[bases]]; q[n_] := Union[(pd = primBase[n])] == Range[0, Length[pd] - 1]; Select[Range[0, max], q]

%Y Cf. A049345, A235224, A343476.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Apr 16 2021