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

Author

Rick L. Shepherd, Nov 15 2014

Keywords

• nonn
• base
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

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 *)

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)