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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A249572 Least positive integer whose decimal digits divide the plane into n+1 regions. Equivalently, least positive integer with n holes in its decimal digits. 11
1, 4, 8, 48, 88, 488, 888, 4888, 8888, 48888, 88888, 488888, 888888, 4888888, 8888888, 48888888, 88888888, 488888888, 888888888, 4888888888, 8888888888, 48888888888, 88888888888, 488888888888, 888888888888, 4888888888888, 8888888888888, 48888888888888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Leading zeros are not permitted. Variations are possible depending upon whether 4 is considered "holey" (if not, replace each "4" with a "6") and whether nonnegative integers are permitted (a(2) becomes 0). In each case, all terms after the first could be considered "wholly holey," as could all terms of A001743 and A001744, as each digit contains a hole (loop). The analogous sequence of bits for base 2 is simply A011557, the powers of 10, read instead as binary numbers, i.e., as powers of two.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Brady Haran and Neil Sloane, What Number Comes Next? (2018), Numberphile video

FORMULA

a(n) = 10*a(n-2) + 8 for n >= 3.

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.: (10*x^3 - 6*x^2 + 3*x + 1)/((x - 1)*(10*x^2 - 1)). (End)

EXAMPLE

This sequence uses "holey" fours. So a(1)=4, because

. . . . . . . . . . . .       . . . . . . . . . . . .

.                     .       .                     .

.           XXXX      .       .    XX       XX      .

.          XX XX      .       .    XX       XX      .

.         XX  XX      .       .    XX       XX      .

.        XX   XX      .       .    XX       XX      .

.       XX    XX      .       .    XX       XX      .

.      XX     XX      .       .    XX       XX      .

.     XX      XX      .       .    XX       XX      .

.    XX       XX      .       .    XX       XX      .

.    XXXXXXXXXXXXX    .       .    XXXXXXXXXXXXX    .

.             XX      .       .             XX      .

.             XX      .       .             XX      .

.             XX      .       .             XX      .

.             XX      .       .             XX      .

.             XX      .       .             XX      .

.                     .       .                     .

.      "Holey" 4      .       .    "Non-holey" 4    .

. . . . . . . . . . . .       . . . . . . . . . . . .

- Jon E. Schoenfield, Nov 15 2014

MAPLE

a:= n-> `if`(n=0, 1, parse(cat(4*(irem(n, 2, 'q')), 8$q))):

seq(a(n), n=0..30);  # Alois P. Heinz, Nov 01 2014

PROG

(MAGMA) I:=[1, 4, 8, 48]; [n le 4 select I[n] else 10*Self(n-2)+8: n in [1..30]]; // Vincenzo Librandi, Nov 17 2014

(PARI) A249572(n)=10^(n\2)*if(n%2, 45-(n>1)*5, 22)\45 \\ "(..., 9-(n>1), 4.4)\9" would be shorter but cause problems beyond realprecision. - M. F. Hasler, Jul 25 2015

CROSSREFS

Cf. A001743, A001744, A001745, A001746, A002282, A011557, A000079.

Sequence in context: A291948 A002470 A087261 * A078236 A054881 A076687

Adjacent sequences:  A249569 A249570 A249571 * A249573 A249574 A249575

KEYWORD

nonn,base,easy

AUTHOR

Rick L. Shepherd, Nov 01 2014

EXTENSIONS

Offset corrected by Brady Haran, Nov 27 2018

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 March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)