A078245 Smallest multiple of n using only digits 0 and 6.

6, 6, 6, 60, 60, 6, 6006, 600, 666, 60, 66, 60, 6006, 6006, 60, 6000, 66606, 666, 66006, 60, 6006, 66, 660606, 600, 600, 6006, 666666666, 60060, 6606606, 60, 666066, 60000, 66, 66606, 60060, 6660, 666, 66006, 6006, 600, 66666, 6006, 6606606, 660, 6660, 660606

Offset: 1

Author

Amarnath Murthy, Nov 23 2002

Keywords

• base
• nonn

Comments

a(n) = min{A204093(k): k > 0 and A204093(k) mod n = 0}. [Reinhard Zumkeller, Jan 10 2012]

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Reinhard Zumkeller)

Crossrefs

Cf. A004290, A078241-A078248, A079339, A096681-A096688.

Programs

Haskell

a078245 n = head [x | x <- tail a204093_list, mod x n == 0]
-- Reinhard Zumkeller, Jan 10 2012

Mathematica

With[{c=Rest[FromDigits/@Tuples[{0,6},10]]},Table[SelectFirst[c,Divisible[ #,n]&],{n,50}]] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Apr 15 2015 *)

Python

def A204093(n): return int(bin(n)[2:].replace('1', '6'))
def a(n):
    k = 1
    while A204093(k)%n: k += 1
    return A204093(k)
print([a(n) for n in range(1, 47)]) # Michael S. Branicky, Jun 06 2021

Extensions

More terms from Ray Chandler, Jul 12 2004