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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 (list; graph; refs; listen; history; text; internal format)
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,...

LINKS

Table of n, a(n) for n=1..28.

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: A044444 A250770 A014640 * A215137 A160844 A256878

Adjacent sequences:  A245584 A245585 A245586 * A245588 A245589 A245590

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Jul 26 2014

STATUS

approved

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Last modified June 14 17:51 EDT 2021. Contains 345037 sequences. (Running on oeis4.)