A084006 Squares arising as a concatenation of k and 9's complement of k.

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

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