A037383 Numbers k such that every base-3 digit of k is a base-7 digit of k.

1, 2, 13, 51, 63, 67, 68, 79, 84, 91, 99, 105, 134, 205, 211, 246, 252, 345, 351, 352, 354, 355, 357, 358, 359, 360, 361, 362, 363, 364, 366, 373, 380, 387, 394, 401, 406, 441, 442, 443, 444, 445, 446, 447, 448, 449, 454, 455, 457

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A007089, A007093.

Cf. A037380, A037381, A037382, A037384, A037385, A037386.

Programs

Haskell

import Data.List ((\\), nub)
a037383 n = a037383_list !! (n-1)
a037383_list = filter f [1..] where
   f x = null $ nub (ds 3 x) \\ nub (ds 7 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

Select[Range[500],Complement[Union[IntegerDigits[#,3]],Union[IntegerDigits[#,7]]]=={}&] (* Harvey P. Dale, Jan 28 2024 *)

PARI

upto(N) = my(s7); [n|n<-[1..N], setunion(Set(digits(n, 3)), s7=Set(digits(n, 7)))==s7]; \\ Ruud H.G. van Tol, May 09 2024