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

1, 6, 8, 68, 88, 688, 888, 6888, 8888, 68888, 88888, 688888, 888888, 6888888, 8888888, 68888888, 88888888, 688888888, 888888888, 6888888888, 8888888888, 68888888888, 88888888888, 688888888888, 888888888888, 6888888888888, 8888888888888, 68888888888888

Offset

1,2

Comments

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.

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

Links

Table of n, a(n) for n=1..28.

Brady Haran and N. J. A. Sloane, What Number Comes Next? (2018), Numberphile video

Index entries for linear recurrences with constant coefficients, signature (1, 10, -10).

Formula

a(n) = 10*a(n-2) + 8 for n >= 4.

From Chai Wah Wu, Jul 12 2016: (Start)

a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 4.

G.f.: x*(10*x^3 - 8*x^2 + 5*x + 1)/((x - 1)*(10*x^2 - 1)). (End)

Example

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.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A249572, A250257, A250258, A001743, A001744, A001745, A001746, A002282.

Sequence in context: A322544 A270038 A284635 * A242490 A216796 A137127

Adjacent sequences: A250253 A250254 A250255 * A250257 A250258 A250259

Keyword

nonn,base,easy

Author

Rick L. Shepherd, Nov 15 2014

Status

approved