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A037406 Numbers k such that every base-8 digit of k is a base-10 digit of k.

%I A037406 #16 Aug 22 2021 09:22:18
%S A037406 1,2,3,4,5,6,7,45,105,127,235,274,365,436,487,614,713,731,1017,1024,
%T A037406 1025,1026,1032,1042,1124,1162,1206,1233,1234,1235,1243,1273,1426,
%U A037406 1462,1603,1630,1653,1723,1737,1739,1743,1753,2048
%N A037406 Numbers k such that every base-8 digit of k is a base-10 digit of k.
%H A037406 Reinhard Zumkeller, <a href="/A037406/b037406.txt">Table of n, a(n) for n = 1..10000</a>
%t A037406 b8dQ[n_]:=Module[{idn=Union[IntegerDigits[n]],idn8=Union[IntegerDigits[n,8]]},And@@Table[MemberQ[idn,idn8[[i]]],{i,Length[idn8]}]]
%t A037406 Select[Range[2100],b8dQ]  (* _Harvey P. Dale_, Feb 27 2011 *)
%o A037406 (Haskell)
%o A037406 import Data.List ((\\), nub)
%o A037406 a037406 n = a037406_list !! (n-1)
%o A037406 a037406_list = filter f [1..] where
%o A037406    f x = null $ nub (ds 8 x) \\ nub (ds 10 x)
%o A037406    ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
%o A037406 -- _Reinhard Zumkeller_, May 30 2013
%o A037406 (Python)
%o A037406 def ok(n): return set(oct(n)[2:]) <= set(str(n))
%o A037406 print(list(filter(ok, range(1, 2049)))) # _Michael S. Branicky_, Aug 22 2021
%Y A037406 Cf. A037405, A037442.
%K A037406 nonn,base
%O A037406 1,2
%A A037406 _Clark Kimberling_