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A217789 Least difference between 2 palindromic numbers of length n.

%I A217789 #20 Jun 29 2023 13:15:39
%S A217789 1,11,10,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
%T A217789 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
%U A217789 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11
%N A217789 Least difference between 2 palindromic numbers of length n.
%C A217789 In his video, Fields medallist Villani asks about the number of palindromes of length n (cf. A050683 and A070252), and the minimal difference among any two of these (this sequence). Except for the 1 and 3-digits case (where e.g. 111-101=10), the minimal difference of 11 appears as 20...02 - 19...91 and similar patterns (1st and last digits increased by 1,...,7). - _M. F. Hasler_, Mar 25 2013
%C A217789 Also, continued fraction expansion of (2695-5*sqrt(5))/2462. [_Bruno Berselli_, Mar 25 2013]
%H A217789 Cédric Villani, <a href="http://www.dailymotion.com/video/xydgi9_les-defis-mathematiques-du-monde-episode-1-les-palindromes_news">Les défis mathématiques du Monde, épisode 1 : les palindromes</a>
%H A217789 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A217789 G.f.: x*(1+10*x-x^2+x^3)/(1-x). [_Bruno Berselli_, Mar 25 2013]
%e A217789 a(1)=1 for instance 8-7.
%e A217789 a(2)=11 for instance 22-11.
%e A217789 a(3)=10 for instance 111-101.
%e A217789 a(n)=11 for n >= 4, for instance 2002-1991, resp. generalization to n digits (cf. comment).
%o A217789 (PARI) A217789(n)=11-(n==3)-(n==1)*10  \\ [_M. F. Hasler_, Mar 25 2013]
%Y A217789 Cf. A050683, A070252.
%K A217789 nonn,easy,base
%O A217789 1,2
%A A217789 _Michel Marcus_, Mar 25 2013