cp's OEIS Frontend

A363377 Largest positive integer having n holes that can be made using the fewest possible digits.

%I A363377 #63 Jun 02 2025 16:49:53
%S A363377 7,9,8,98,88,988,888,9888,8888,98888,88888,988888,888888,9888888,
%T A363377 8888888,98888888,88888888,988888888,888888888,9888888888,8888888888,
%U A363377 98888888888,88888888888,988888888888,888888888888,9888888888888,8888888888888,98888888888888,88888888888888,988888888888888
%N A363377 Largest positive integer having n holes that can be made using the fewest possible digits.
%C A363377 Each decimal digit has 0, 1 or 2 holes so that n holes requires A065033(n) digits.
%H A363377 <a href="/index/Ho#holes">Index entries for sequences related to holes in digits</a>.
%H A363377 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F A363377 From _Natalia L. Skirrow_, Jun 26 2023: (Start)
%F A363377 a(n) = (89*(10^((n-1)/2))-8)/9 for odd n; a(n) = 8*(10^(n/2)-1)/9 for even n >= 2.
%F A363377 a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3), for n >= 4.
%F A363377 G.f.: (7+2*x-71*x^2+70*x^3)/((1-x)*(1-10*x^2)).
%F A363377 E.g.f.: (80*cosh(sqrt(10)*x) + 89*sqrt(10)*sinh(sqrt(10)*x) - 80*e^x)/90 + 7. (End)
%e A363377 For n=0, the largest integer with no holes in it that is as short as possible is 7 (9 is larger, but has 1 hole; 11 is larger and has no holes, but is longer at length 2 > length 1).
%e A363377 For n=1, the largest integer with 1 hole that is as short as possible is 9 (following the same kind of reasoning as with n=0).
%t A363377 CoefficientList[Series[(7 + 2 x - 71 x^2 + 70 x^3)/((1 - x) (1 - 10 x^2)), {x, 0, 30}], x] (* _Michael De Vlieger_, Jul 05 2023 *)
%o A363377 (Python)
%o A363377 A363377=lambda n: (8+n%2*81)*10**(n>>1)//9 if n else 7
%o A363377 print([A363377(n) for n in range(30)]) # _Natalia L. Skirrow_, Jun 26 2023
%Y A363377 Cf. A002281 and A002282 (number of holes), A065033 (digits required).
%Y A363377 Cf. A249572 and A250256 (smallest number).
%Y A363377 Cf. A337099 (largest 7-segment).
%K A363377 nonn,base,easy
%O A363377 0,1
%A A363377 _Julia Zimmerman_, May 29 2023