A093220 a(n) is the largest number such that all of a(n)'s length-n substrings are distinct and divisible by 20.

0, 800, 98000, 9980000, 999800000, 99998000000, 9999980000000, 999999800000000, 99999998000000000, 9999999980000000000, 999999999800000000000, 99999999998000000000000, 9999999999980000000000000, 999999999999800000000000000, 99999999999998000000000000000

Offset

1,2

Comments

For n > 1, a(n) is n-2 9's followed by an 8, followed by n 0's. - John Cerkan, May 23 2017

Links

Table of n, a(n) for n=1..15.

Hans Havermann, Table of A093211-A093299

Index entries for linear recurrences with constant coefficients, signature (10, -20).

Formula

From Chai Wah Wu, Oct 25 2018: (Start)

a(n) = 110*a(n-1) - 1000*a(n-2) for n > 3.

G.f.: 400*x^2*(25*x + 2)/((10*x - 1)*(100*x - 1)). (End)

Example

a(3) is 98000 because its length-3 substrings (980, 800, 000) are all distinct and divisible by 20 and there is no larger number with this property

Prog

(GAP) a:=[800, 98000];; for n in [3..12] do a[n]:=110*a[n-1]-1000*a[n-2]; od; Concatenation([0], a); # Muniru A Asiru, Oct 25 2018
(PARI) concat(0, Vec(400*x^2*(25*x + 2)/((10*x - 1)*(100*x - 1)) + O(x^20))) \\ Felix Fröhlich, Oct 25 2018

Crossrefs

Cf. A093211, A093212, ..., A093299.

Sequence in context: A097206 A093280 A093240 * A035757 A023100 A107553

Adjacent sequences: A093217 A093218 A093219 * A093221 A093222 A093223

Keyword

base,nonn

Author

Hans Havermann, Mar 28 2004

Extensions

a(8)-a(10) from John Cerkan, May 23 2017

More terms from Felix Fröhlich, Oct 25 2018

Status

approved