|
%I #28 Aug 06 2020 01:02:36
%S 3,6,30,60,300,600,3000,6000,30000,60000,300000,600000,3000000,
%T 6000000,30000000,60000000,300000000,600000000,3000000000,6000000000,
%U 30000000000,60000000000,300000000000,600000000000,3000000000000,6000000000000,30000000000000,60000000000000,300000000000000
%N a(n) is the minimal difference between two distinct n-digit numbers with 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_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,10).
%F If n is even, a(n) is 6 followed by (n - 2) / 2 zeros. If n is odd, a(n) is 3 followed by (n - 1) / 2 zeros.
%F So a(n) = 3 * 10^(floor(n-1)/2) * 2^(1 - n (mod 2)).
%F From _David A. Corneth_, Aug 05 2020: (Start)
%F a(n) = 10*a(n - 2) for n > 2.
%F G.f.: (3*x + 6*x^2)/(1 - 10*x^2). (End)
%e a(3) = 30. If one types 595 into a calculator and rotates it 180 degrees, they will get 565. 595 - 565 = 30. With a little thought, it is provable that 30 is the smallest possible difference.
%t LinearRecurrence[{0, 10}, {3, 6}, 30] (* _Amiram Eldar_, Aug 05 2020 *)
%o (PARI) first(n) = my(res = List([3, 6])); for(i = #res + 1, n, listput(res, 10*res[#res-1])); res \\ _David A. Corneth_, Aug 05 2020
%Y Cf. A125520 (maximal difference).
%K nonn,easy,base
%O 1,1
%A _Tanya Khovanova_ and Sergei Bernstein, Dec 29 2006
|
