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

1, 2, 3, 4, 5, 6, 7, 45, 105, 127, 235, 274, 365, 436, 487, 614, 713, 731, 1017, 1024, 1025, 1026, 1032, 1042, 1124, 1162, 1206, 1233, 1234, 1235, 1243, 1273, 1426, 1462, 1603, 1630, 1653, 1723, 1737, 1739, 1743, 1753, 2048

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037405, A037442.

Programs

Haskell

import Data.List ((\\), nub)
a037406 n = a037406_list !! (n-1)
a037406_list = filter f [1..] where
   f x = null $ nub (ds 8 x) \\ nub (ds 10 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

Mathematica

b8dQ[n_]:=Module[{idn=Union[IntegerDigits[n]],idn8=Union[IntegerDigits[n,8]]},And@@Table[MemberQ[idn,idn8[[i]]],{i,Length[idn8]}]]
Select[Range[2100],b8dQ]  (* Harvey P. Dale, Feb 27 2011 *)

Python

def ok(n): return set(oct(n)[2:]) <= set(str(n))
print(list(filter(ok, range(1, 2049)))) # Michael S. Branicky, Aug 22 2021