login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279193 Least positive integer whose decimal digits divide the plane into n regions (version for people who write 2 with a curlicue). 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)