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

1,1

Links

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A233472 A284596 A216485 * A247793 A067276 A118580

Adjacent sequences: A096678 A096679 A096680 * A096682 A096683 A096684

Keyword

base,nonn

Author

Ray Chandler, Jul 12 2004

Status

approved