A245385 Numbers N such that N = P//Q = R//S, where // is the concatenation function, satisfying the following properties: P and S are m-digit integers, Q and R are k-digit integers, k and m are distinct positive integers, and P*Q = R*S.

111, 164, 195, 222, 265, 333, 444, 498, 555, 666, 777, 888, 999, 1111, 1664, 1995, 2222, 2665, 3333, 4444, 4847, 4998, 5555, 6545, 6666, 7424, 7777, 8888, 9999, 11111, 16664, 19995, 21775, 22222, 24996, 26665, 33333, 43243, 44444, 49998, 55555, 66666, 77777, 86486, 88888, 99999

Offset: 1

Author

Derek Orr, Jul 20 2014

Keywords

• nonn
• base

Examples

			Take the number 21775.
2*1775 != 2177*5.
21*775 == 217*75 = 16275. Thus 21775 is a member of this sequence.
		

Crossrefs

Cf. A245364, A245386.

Programs

Python

for n in range(1,10**5):
  s = str(n)
  count = 0
  for i in range(1,len(s)):
    num = int(s[:i])*int(s[i:])
    if i != len(s) - i:
      if num != 0:
        if num == int(s[:len(s)-i])*int(s[len(s)-i:]):
          count += 1
          break
  if count > 0:
    print(n,end=', ')