

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
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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(n1) + 10*a(n2)  10*a(n3) 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(n1)+10*Self(n2)10*Self(n3): 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



