

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



FORMULA

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



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



