%I #22 Nov 13 2021 14:29:33
%S 3,75,825,8835,89235,898335,8992335,89983335,899923335,8999833335,
%T 89999233335,899998333335,8999992333335,89999983333335,
%U 899999923333335,8999999833333335,89999999233333335,899999998333333335,8999999992333333335,89999999983333333335,899999999923333333335
%N a(n) is the maximal difference between two distinct n-digit numbers with the property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen.
%H <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,0,-110,100).
%F If n is greater than 2 and even, than a(n) is 8 followed by (n / 2) - 2 nines followed by another 8 followed by (n / 2) - 1 threes followed by 5. If n is greater than 2 and odd, than a(n) is 8 followed by (n / 2) - 1.5 nines followed by a 2 followed by (n / 2) - 1.5 threes followed by a 5.
%e a(2) = 75. If someone types 91 into a calculator and rotates it 180 degrees, they will get 16. 91 - 16 = 75. It is easy to check that no larger differences can be obtained.
%t LinearRecurrence[{11,0,-110,100},{3,75,825,8835},30] (* _Harvey P. Dale_, Nov 13 2021 *)
%o (PARI) first(n) = {my(res = List([3, 75, 825, 8835, 89235, 898335, 8992335, 89983335])); for(i = #res + 1, n, listput(res, 11*res[#res] - 110*res[#res-2] + 100 * res[#res-3])); res} \\ _David A. Corneth_, Aug 05 2020
%Y Cf. A125521 (minimal difference).
%K nonn,easy,base
%O 1,1
%A _Tanya Khovanova_ and Sergei Bernstein, Dec 29 2006