cp's OEIS Frontend

A250258 Least nonnegative integer whose decimal digits divide the plane into n regions (A250257 variant).

%I A250258 #20 Jun 28 2023 08:38:34
%S A250258 1,0,8,68,88,688,888,6888,8888,68888,88888,688888,888888,6888888,
%T A250258 8888888,68888888,88888888,688888888,888888888,6888888888,8888888888,
%U A250258 68888888888,88888888888,688888888888,888888888888,6888888888888,8888888888888,68888888888888
%N A250258 Least nonnegative integer whose decimal digits divide the plane into n regions (A250257 variant).
%C A250258 Equivalently, with offset 0, least nonnegative integer with n holes in its decimal digits. Leading zeros are not permitted. Variation of A250257 with the numeral "4" considered open at the top, as it is often handwritten. See also the comments in A249572.
%H A250258 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 10, -10).
%F A250258 a(n) = 10*a(n-2) + 8 for n >= 5.
%F A250258 a(n) = A250256(n), n<>2.
%F A250258 From _Chai Wah Wu_, Jul 12 2016: (Start)
%F A250258 a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 5.
%F A250258 G.f.: x*(-60*x^4 + 70*x^3 - 2*x^2 - x + 1)/((x - 1)*(10*x^2 - 1)). (End)
%e A250258 The integer 68, whose decimal digits have 3 holes, divides the plane into 4 regions. No smaller nonnegative integer does this, so a(4) = 68.
%t A250258 Join[{1, 0, 8}, RecurrenceTable[{a[1]==68, a[2]==88, a[n]==10 a[n-2] + 8}, a, {n, 20}]] (* _Vincenzo Librandi_, Nov 16 2014 *)
%o A250258 (Magma) I:=[1,0,8,68,88]; [n le 5 select I[n] else 10*Self(n-2)+8: n in [1..40]]; // _Vincenzo Librandi_, Nov 16 2014
%Y A250258 Cf. A249572, A250256, A250257, A001743, A001744, A001745, A001746, A002282.
%K A250258 nonn,base,easy
%O A250258 1,3
%A A250258 _Rick L. Shepherd_, Nov 15 2014