This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A249572 #73 Jun 15 2025 01:32:40
%S A249572 1,4,8,48,88,488,888,4888,8888,48888,88888,488888,888888,4888888,
%T A249572 8888888,48888888,88888888,488888888,888888888,4888888888,8888888888,
%U A249572 48888888888,88888888888,488888888888,888888888888,4888888888888,8888888888888,48888888888888
%N 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.
%C A249572 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.
%H A249572 Alois P. Heinz, <a href="/A249572/b249572.txt">Table of n, a(n) for n = 0..2000</a>
%H A249572 Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=OeGSQggDkxI">What Number Comes Next?</a> (2018), Numberphile video.
%H A249572 Julia Witte Zimmerman, Denis Hudon, Kathryn Cramer, Jonathan St. Onge, Mikaela Fudolig, Milo Z. Trujillo, Christopher M. Danforth, and Peter Sheridan Dodds, <a href="https://arxiv.org/abs/2306.06794">A blind spot for large language models: Supradiegetic linguistic information</a>, arXiv:2306.06794 [cs.CL], 2023.
%H A249572 <a href="/index/Ho#holes">Index entries for sequences related to holes in digits</a>
%H A249572 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F A249572 a(n) = 10*a(n-2) + 8 for n >= 3.
%F A249572 From _Chai Wah Wu_, Dec 14 2016: (Start)
%F A249572 a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 4.
%F A249572 G.f.: (10*x^3 - 6*x^2 + 3*x + 1)/((x - 1)*(10*x^2 - 1)). (End)
%F A249572 a(n) = (2/9)*(10^(n/2)*(4*((n+1) mod 2) + 11*sqrt(2/5)*(n mod 2)) - 4) for n >= 1. - _Alan Michael Gómez Calderón_, May 04 2025
%e A249572 From _Jon E. Schoenfield_, Nov 15 2014: (Start)
%e A249572 This sequence uses "holey" fours. So a(1)=4, because
%e A249572 . . . . . . . . . . . . . . . . . . . . . . . .
%e A249572 . . . .
%e A249572 . XXXX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XX XX . . XX XX .
%e A249572 . XXXXXXXXXXXXX . . XXXXXXXXXXXXX .
%e A249572 . XX . . XX .
%e A249572 . XX . . XX .
%e A249572 . XX . . XX .
%e A249572 . XX . . XX .
%e A249572 . XX . . XX .
%e A249572 . . . .
%e A249572 . "Holey" 4 . . "Non-holey" 4 .
%e A249572 . . . . . . . . . . . . . . . . . . . . . . . . (End)
%p A249572 a:= n-> `if`(n=0, 1, parse(cat(4*(irem(n, 2, 'q')), 8$q))):
%p A249572 seq(a(n), n=0..30); # _Alois P. Heinz_, Nov 01 2014
%t A249572 LinearRecurrence[{1,10,-10},{1,4,8,48},50] (* _Paolo Xausa_, May 31 2023 *)
%o A249572 (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
%o A249572 (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
%Y A249572 Cf. A001743, A001744, A001745, A001746, A002282, A011557, A000079.
%Y A249572 The analogous sequence using 6 instead of 4 is A250256. - _N. J. A. Sloane_, Sep 27 2019
%K A249572 nonn,base,easy
%O A249572 0,2
%A A249572 _Rick L. Shepherd_, Nov 01 2014
%E A249572 Offset corrected by Brady Haran, Nov 27 2018