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%I #20 Jun 29 2023 13:15:39
%S 1,11,10,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
%T 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
%U 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11
%N Least difference between 2 palindromic numbers of length n.
%C 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 Also, continued fraction expansion of (2695-5*sqrt(5))/2462. [_Bruno Berselli_, Mar 25 2013]
%H 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 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F G.f.: x*(1+10*x-x^2+x^3)/(1-x). [_Bruno Berselli_, Mar 25 2013]
%e a(1)=1 for instance 8-7.
%e a(2)=11 for instance 22-11.
%e a(3)=10 for instance 111-101.
%e a(n)=11 for n >= 4, for instance 2002-1991, resp. generalization to n digits (cf. comment).
%o (PARI) A217789(n)=11-(n==3)-(n==1)*10 \\ [_M. F. Hasler_, Mar 25 2013]
%Y Cf. A050683, A070252.
%K nonn,easy,base
%O 1,2
%A _Michel Marcus_, Mar 25 2013
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