cp's OEIS Frontend

A250256 Least positive integer whose decimal digits divide the plane into n regions (A249572 variant).

%I A250256 #23 Aug 12 2025 04:30:52
%S A250256 1,6,8,68,88,688,888,6888,8888,68888,88888,688888,888888,6888888,
%T A250256 8888888,68888888,88888888,688888888,888888888,6888888888,8888888888,
%U A250256 68888888888,88888888888,688888888888,888888888888,6888888888888,8888888888888,68888888888888
%N A250256 Least positive integer whose decimal digits divide the plane into n regions (A249572 variant).
%C A250256 Equivalently, with offset 0, least positive integer with n holes in its decimal digits. Leading zeros are not permitted. Variation of A249572 with the numeral "4" considered open at the top, as it is often handwritten. See also the comments in A249572.
%C A250256 For n > 2, a(n) + a(n+1) divides the plane into 2 regions. For n > 1, a(2n) - a(2n-1) divides the plane into n+1 regions. For n >= 1, a(2n+1) - a(2n) divides the plane into n regions. - _Ivan N. Ianakiev_, Feb 23 2015
%H A250256 Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=OeGSQggDkxI">What Number Comes Next?</a> (2018), Numberphile video
%H A250256 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F A250256 a(n) = 10*a(n-2) + 8 for n >= 4.
%F A250256 From _Chai Wah Wu_, Jul 12 2016: (Start)
%F A250256 a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 4.
%F A250256 G.f.: x*(10*x^3 - 8*x^2 + 5*x + 1)/((x - 1)*(10*x^2 - 1)). (End)
%F A250256 E.g.f.: (9 + 45*x - 40*cosh(x) + 31*cosh(sqrt(10)*x) - 40*sinh(x) + 4*sqrt(10)*sinh(sqrt(10)*x))/45. - _Stefano Spezia_, Aug 11 2025
%e A250256 The integer 68, whose decimal digits have 3 holes, divides the plane into 4 regions. No smaller positive integer does this, so a(4) = 68.
%t A250256 Join[{1, 6, 8}, RecurrenceTable[{a[1]==68, a[2]==88, a[n]==10 a[n-2] + 8}, a, {n, 20}]] (* _Vincenzo Librandi_, Nov 16 2014 *)
%o A250256 (Magma) I:=[1,6,8,68]; [n le 4 select I[n] else 10*Self(n-2)+8: n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2014
%Y A250256 Cf. A249572, A250257, A250258, A001743, A001744, A001745, A001746, A002282.
%K A250256 nonn,base,easy
%O A250256 1,2
%A A250256 _Rick L. Shepherd_, Nov 15 2014