A250257 Least nonnegative integer whose decimal digits divide the plane into n regions.

1, 0, 8, 48, 88, 488, 888, 4888, 8888, 48888, 88888, 488888, 888888, 4888888, 8888888, 48888888, 88888888, 488888888, 888888888, 4888888888, 8888888888, 48888888888, 88888888888, 488888888888, 888888888888, 4888888888888, 8888888888888, 48888888888888

Offset

1,3

Comments

Equivalently, with offset 0, least nonnegative integer with n holes in its decimal digits. Leading zeros are not permitted. Identical to A249572 except that a(2) = 0, not 4. See also the comments in A249572.

Links

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

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

Formula

a(n) = 10*a(n-2) + 8 for n >= 5.

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

a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 5.

G.f.: x*(-40*x^4 + 50*x^3 - 2*x^2 - x + 1)/((x - 1)*(10*x^2 - 1)). (End)

Example

The integer 48, whose decimal digits have 3 holes, divides the plane into 4 regions. No smaller nonnegative integer does this, so a(4) = 48.

Mathematica

Join[{1, 0, 8}, RecurrenceTable[{a[1]==48, a[2]==88, a[n]==10 a[n-2] + 8}, a, {n, 20}]] (* Vincenzo Librandi, Nov 16 2014 *)

Prog

(Magma) I:=[1, 0, 8, 48, 88]; [n le 5 select I[n] else 10*Self(n-2)+8: n in [1..30]]; // Vincenzo Librandi, Nov 15 2014

Crossrefs

Cf. A249572, A250256, A250258, A001743, A001744, A001745, A001746, A002282.

Sequence in context: A165037 A121028 A139279 * A067239 A152750 A121355

Adjacent sequences: A250254 A250255 A250256 * A250258 A250259 A250260

Keyword

nonn,base,easy

Author

Rick L. Shepherd, Nov 15 2014

Status

approved