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

Robert Israel, Table of n, a(n) for n = 1..367

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

Cf. A007913, A046412, A084004, A084005, A084007.

Sequence in context: A257649 A259240 A341555 * A254648 A202330 A226264

Adjacent sequences:  A084003 A084004 A084005 * A084007 A084008 A084009

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

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)