A279193 Least positive integer whose decimal digits divide the plane into n regions (version for people who write 2 with a curlicue).

1, 2, 8, 28, 88, 288, 888, 2888, 8888, 28888, 88888, 288888, 888888, 2888888, 8888888, 28888888, 88888888, 288888888, 888888888, 2888888888, 8888888888, 28888888888, 88888888888, 288888888888, 888888888888, 2888888888888, 8888888888888, 28888888888888

Offset

1,2

Comments

Equivalently, with offset 0, least positive integer with n holes in its decimal digits. Note that 2 written with a curlicue has one hole, 8 has two holes, 28 has three holes, etc., as in the illustration. See A249572 and A250256 for other versions.

Links

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

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

N. J. A. Sloane, Illustration of initial terms.

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

Formula

From Chai Wah Wu, Dec 14 2016: (Start)

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

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

a(n) = ((26 - (13 - 4*sqrt(10))*(1 - (-1)^n))*sqrt(10^n) - 80)/90 for n>1, a(1)=1. - Bruno Berselli, Dec 15 2016

Mathematica

Join[{1}, LinearRecurrence[{1, 10, -10}, {2, 8, 28}, 30]] (* Vincenzo Librandi, Dec 15 2016 *)

Prog

(Magma) I:=[1, 2, 8, 28]; [n le 4 select I[n] else Self(n-1)+10*Self(n-2)-10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 15 2016

Crossrefs

See A249572, A250256 for other versions.

Sequence in context: A176758 A178222 A090426 * A280279 A060995 A106731

Adjacent sequences: A279190 A279191 A279192 * A279194 A279195 A279196

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Dec 14 2016, following a suggestion from Colin Stewart

Status

approved