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 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

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