|
%I #10 Jul 23 2014 10:27:21
%S 111,164,195,222,265,333,444,498,555,666,777,888,999,1111,1664,1995,
%T 2222,2665,3333,4444,4847,4998,5555,6545,6666,7424,7777,8888,9999,
%U 11111,16664,19995,21775,22222,24996,26665,33333,43243,44444,49998,55555,66666,77777,86486,88888,99999
%N 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 Take the number 21775.
%e 2*1775 != 2177*5.
%e 21*775 == 217*75 = 16275. Thus 21775 is a member of this sequence.
%o (Python)
%o for n in range(1,10**5):
%o ..s = str(n)
%o ..count = 0
%o ..for i in range(1,len(s)):
%o ....num = int(s[:i])*int(s[i:])
%o ....if i != len(s) - i:
%o ......if num != 0:
%o ........if num == int(s[:len(s)-i])*int(s[len(s)-i:]):
%o ..........count += 1
%o ..........break
%o ..if count > 0:
%o ....print(n,end=', ')
%Y Cf. A245364, A245386.
%K nonn,base
%O 1,1
%A _Derek Orr_, Jul 20 2014
|
