A096681 Least k such that decimal representation of k*n contains only digits 0 and 2.

2, 1, 74, 5, 4, 37, 286, 25, 24691358, 2, 2, 185, 154, 143, 148, 125, 1306, 12345679, 1158, 1, 962, 1, 9574, 925, 8, 77, 81563786, 715, 75938, 74, 7162, 625, 6734, 653, 572, 61728395, 6, 579, 518, 5, 542, 481, 51214, 5, 49382716, 4787, 426, 4625, 44898, 4

Offset: 1

Author

Ray Chandler, Jul 12 2004

Keywords

• base
• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004290, A078241-A078248, A079339, A096682, A096683, A096684, A096685, A096686, A096687, A096688.

Programs

PARI

isok(n) = my(vd = vecsort(digits(n),,8)); (vd == [0,2]) || (vd == [2]);
a(n) = my(k=1); while(!isok(k*n), k++); k; \\ Michel Marcus, Sep 25 2016

Python

def next02(n):
  s = str(n)
  if s > '2'*len(s): return int('2' + '0'*len(s))
  for i, c in enumerate(s):
    if c == '1': return int(s[:i] + '2' + '0'*(len(s)-i-1))
    elif s[i:] > '2'*(len(s)-i): return int(s[:i-1] + '2' + '0'*(len(s)-i))
def a(n):
  k = 1
  while set(str(k*n)) - set('02') != set(): k = max(k+1, next02(k*n)//n)
  return k
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Feb 01 2021

Formula

a(n) = A078241(n)/n.