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A245587 Let x(1)x(2)... x(2q) denote the decimal expansion of a number n with an even number of digits. The sequence lists the numbers n such that (10^q-a)*(10^q-b) = n where a is the number having the digits x(1)x(2)...x(q) and b is the number having the digits x(q+1)x(q+2)...x(2q). 0

%I #19 Sep 06 2014 00:45:12

%S 18,35,50,1680,2664,3350,4130,5000,166800,251664,333500,401330,500000,

%T 16668000,25016664,33335000,40013330,50000000,1666680000,2500166664,

%U 3333350000,4000133330,5000000000,166666800000,250001666664,333333500000,400001333330,500000000000

%N Let x(1)x(2)... x(2q) denote the decimal expansion of a number n with an even number of digits. The sequence lists the numbers n such that (10^q-a)*(10^q-b) = n where a is the number having the digits x(1)x(2)...x(q) and b is the number having the digits x(q+1)x(q+2)...x(2q).

%C Numbers n with 2*q digits in base 10 such that (10^q - floor(n/10^q))*(10^q - n modulo 10^q) = n.

%C The sequence is infinite and contains five subsequences having the following properties:

%C Subsequence 18, 1680, 166800, 16668000, 1666680000,...

%C Subsequence 35, 3350, 333500, 33335000, 3333350000,...

%C Subsequence 50, 5000, 500000, 50000000, 5000000000,...

%C Subsequence 2664, 251664, 25016664, 2500166664, 250001666664,...

%C Subsequence 4130, 401330, 40013330, 4000133330, 400001333330,...

%e 35 is in the sequence because (10-3)*(10-5) = 7*5 = 35;

%e 2664 is in the sequence because (100-26)*(100-64) = 74*36 = 2664.

%p for n from 1 by 2 to 15 do:for k from 10^n to 10^(n+1)-1 do: n1:=(n+1)/2:a1:= irem(k,10^n1):b1:=(k-a1)/10^n1:a:=10^n1-a1:b:=10^n1-b1:if a*b=k then printf(`%d, `,k):else fi:od:od:

%o (PARI) lista(nn) = {forstep (k=1, nn, 2, for (n= 10^k, 10^(k+1)-1, pq = 10^((k+1)/2); if ((pq - (n % pq))*(pq - n\pq) == n, print1(n, ", "));););} \\ _Michel Marcus_, Aug 28 2014

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Jul 26 2014

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)