cp's OEIS Frontend

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.

%I A245385 #12 May 22 2025 10:21:39
%S A245385 111,164,195,222,265,333,444,498,555,666,777,888,999,1111,1664,1995,
%T A245385 2222,2665,3333,4444,4847,4998,5555,6545,6666,7424,7777,8888,9999,
%U A245385 11111,16664,19995,21775,22222,24996,26665,33333,43243,44444,49998,55555,66666,77777,86486,88888,99999
%N 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.
%e A245385 Take the number 21775.
%e A245385 2*1775 != 2177*5.
%e A245385 21*775 == 217*75 = 16275. Thus 21775 is a member of this sequence.
%o A245385 (Python)
%o A245385 for n in range(1,10**5):
%o A245385   s = str(n)
%o A245385   count = 0
%o A245385   for i in range(1,len(s)):
%o A245385     num = int(s[:i])*int(s[i:])
%o A245385     if i != len(s) - i:
%o A245385       if num != 0:
%o A245385         if num == int(s[:len(s)-i])*int(s[len(s)-i:]):
%o A245385           count += 1
%o A245385           break
%o A245385   if count > 0:
%o A245385     print(n,end=', ')
%Y A245385 Cf. A245364, A245386.
%K A245385 nonn,base
%O A245385 1,1
%A A245385 _Derek Orr_, Jul 20 2014