OFFSET
1,2
COMMENTS
Equivalently, with offset 0, least positive integer with n holes in its decimal digits. Leading zeros are not permitted. Variation of A249572 with the numeral "4" considered open at the top, as it is often handwritten. See also the comments in A249572.
For n > 2, a(n) + a(n+1) divides the plane into 2 regions. For n > 1, a(2n) - a(2n-1) divides the plane into n+1 regions. For n >= 1, a(2n+1) - a(2n) divides the plane into n regions. - Ivan N. Ianakiev, Feb 23 2015
LINKS
Brady Haran and N. J. A. Sloane, What Number Comes Next? (2018), Numberphile video
Index entries for linear recurrences with constant coefficients, signature (1, 10, -10).
FORMULA
a(n) = 10*a(n-2) + 8 for n >= 4.
From Chai Wah Wu, Jul 12 2016: (Start)
a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 4.
G.f.: x*(10*x^3 - 8*x^2 + 5*x + 1)/((x - 1)*(10*x^2 - 1)). (End)
EXAMPLE
The integer 68, whose decimal digits have 3 holes, divides the plane into 4 regions. No smaller positive integer does this, so a(4) = 68.
MATHEMATICA
Join[{1, 6, 8}, RecurrenceTable[{a[1]==68, a[2]==88, a[n]==10 a[n-2] + 8}, a, {n, 20}]] (* Vincenzo Librandi, Nov 16 2014 *)
PROG
(Magma) I:=[1, 6, 8, 68]; [n le 4 select I[n] else 10*Self(n-2)+8: n in [1..30]]; // Vincenzo Librandi, Nov 15 2014
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Rick L. Shepherd, Nov 15 2014
STATUS
approved