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A084006
Squares arising as a concatenation of k and 9's complement of k.
6
36, 81, 1089, 4356, 9801, 110889, 443556, 998001, 11108889, 44435556, 99980001, 1111088889, 4444355556, 9999800001, 111110888889, 444443555556, 999998000001, 11111108888889, 44444435555556, 99999980000001
OFFSET
1,1
COMMENTS
From Robert Israel, Sep 09 2020: (Start)
Numbers of the form j^2*x*(10^k-1) where x = A007913(10^k-1) and 10^(k-1)+1 <= j^2*x <= 10^k-1.
If k >= 2 is not in A046412, there are only three terms with 2*k digits, namely (10^k-1)^2/9, 4*(10^k-1)^2/9, and 9*(10^k-1)^2/9.
The first term not of one of those three forms is a(25)=197530863802469136.
(End)
LINKS
EXAMPLE
1089 = 33^2 is a concatenation of 10 and 89, 10+89 = 99.
MAPLE
f:= proc(k) local F, x, p, t;
p:= 10^k-1;
F:= select(t -> t[2]::odd, ifactors(p)[2]);
x:= mul(t[1], t=F);
seq(j^2*x*p, j=ceil(sqrt((10^(k-1)+1)/x))..floor(sqrt(p/x)))
end proc:
map(f, [$1..20]); # Robert Israel, Sep 09 2020
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 23 2003
EXTENSIONS
More terms from Ray Chandler, May 31 2003
Offset changed by Robert Israel, Sep 09 2020
STATUS
approved