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A116098
Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 6.
6
11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 13223140496, 20661157025, 29752066116, 40495867769, 52892561984, 66942148761, 82644628100, 100000000001, 1000000000001
OFFSET
1,1
COMMENTS
From Robert Israel, Aug 13 2018: (Start)
Contained in, and apparently identical, to A116129.
Numbers k such that k*(10^d+1) is a square, where k-9 has d decimal digits.
(End)
LINKS
EXAMPLE
100000001//99999992 = 99999998 * 100000004, where // denotes
concatenation.
MAPLE
g:= proc(d) local r, c, a, b;
r:= mul(t[1], t=select(s -> s[2]::odd, ifactors(10^d+1)[2]))
c:= ceil((10^(d-1)+9)/r);
a:= isqrt(c);
if a^2 < c then a:= a+1 fi;
c:= floor((10^d+8)/r);
b:= isqrt(c);
if b^2 > c then b:= b-1 fi;
seq(r*y^2, y = a..b)
end proc:
seq(g(d), d=1..60); # Robert Israel, Aug 13 2018
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved