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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
18, 35, 50, 1680, 2664, 3350, 4130, 5000, 166800, 251664, 333500, 401330, 500000, 16668000, 25016664, 33335000, 40013330, 50000000, 1666680000, 2500166664, 3333350000, 4000133330, 5000000000, 166666800000, 250001666664, 333333500000, 400001333330, 500000000000
OFFSET
1,1
COMMENTS
Numbers n with 2*q digits in base 10 such that (10^q - floor(n/10^q))*(10^q - n modulo 10^q) = n.
The sequence is infinite and contains five subsequences having the following properties:
Subsequence 18, 1680, 166800, 16668000, 1666680000,...
Subsequence 35, 3350, 333500, 33335000, 3333350000,...
Subsequence 50, 5000, 500000, 50000000, 5000000000,...
Subsequence 2664, 251664, 25016664, 2500166664, 250001666664,...
Subsequence 4130, 401330, 40013330, 4000133330, 400001333330,...
EXAMPLE
35 is in the sequence because (10-3)*(10-5) = 7*5 = 35;
2664 is in the sequence because (100-26)*(100-64) = 74*36 = 2664.
MAPLE
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:
PROG
(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
CROSSREFS
Sequence in context: A250770 A014640 A238240 * A215137 A160844 A256878
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jul 26 2014
STATUS
approved