A078241 Smallest multiple of n using only digits 0 and 2.

2, 2, 222, 20, 20, 222, 2002, 200, 222222222, 20, 22, 2220, 2002, 2002, 2220, 2000, 22202, 222222222, 22002, 20, 20202, 22, 220202, 22200, 200, 2002, 2202222222, 20020, 2202202, 2220, 222022, 20000, 222222, 22202, 20020, 2222222220, 222

Offset: 1

Author

Amarnath Murthy, Nov 23 2002

Keywords

• base
• nonn

Comments

a(n) = min{A169965(k): k > 1 and A169965(k) mod n = 0}. - Reinhard Zumkeller, Jan 10 2012

Links

• Reinhard Zumkeller and Chai Wah Wu, Table of n, a(n) for n = 1..9998 First 998 terms from Reinhard Zumkeller.

Crossrefs

Cf. A004290, A078242-A078248, A079339, A096681-A096688, A181060, A181061, A216481, A216812.

Programs

Haskell

a078241 n = head [x | x <- tail a169965_list, mod x n == 0]
-- Reinhard Zumkeller, Jan 10 2012

Mathematica

Module[{m=Rest[FromDigits/@Tuples[{0,2},12]]},Table[Select[m,Divisible[ #,n]&,1],{n,40}]]//Flatten (* Harvey P. Dale, Jul 31 2017 *)

Python

def A078241(n):
    if n > 0:
        for i in range(1,2**n):
            x = 2*int(bin(i)[2:])
            if not x % n:
                return x
    return 0 # Chai Wah Wu, Dec 30 2014

Formula

a(n) < 10^n / (0.45 n). - Charles R Greathouse IV, Jan 09 2012

a(n) <= A216812(n) <= 2(10^n - 1)/9. - N. J. A. Sloane, Sep 18 2012

Extensions

More terms from Ray Chandler, Jul 12 2004