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

1, 0, 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

1,3

Comments

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.

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.

a(n) = A250256(n), n<>2.

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*(-60*x^4 + 70*x^3 - 2*x^2 - 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 nonnegative integer does this, so a(4) = 68.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A249572, A250256, A250257, A001743, A001744, A001745, A001746, A002282.

Sequence in context: A363309 A000434 A304073 * A192091 A050841 A208947

Adjacent sequences: A250255 A250256 A250257 * A250259 A250260 A250261

Keyword

nonn,base,easy

Author

Rick L. Shepherd, Nov 15 2014

Status

approved