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 A217789 Least difference between 2 palindromic numbers of length n. 1
 1, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 Also, continued fraction expansion of (2695-5*sqrt(5))/2462. [Bruno Berselli, Mar 25 2013] LINKS Cédric Villani, Les défis mathématiques du Monde, épisode 1 : les palindromes FORMULA G.f.: x*(1+10*x-x^2+x^3)/(1-x). [Bruno Berselli, Mar 25 2013] EXAMPLE a(1)=1 for instance 8-7. a(2)=11 for instance 22-11. a(3)=10 for instance 111-101. a(n)=11 for n >= 4, for instance 2002-1991, resp. generalization to n digits (cf. comment). PROG (PARI) A217789(n)=11-(n==3)-(n==1)*10  \\ [M. F. Hasler, Mar 25 2013] CROSSREFS Cf. A050683, A070252. Sequence in context: A059941 A086100 A182782 * A004283 A106421 A019329 Adjacent sequences:  A217786 A217787 A217788 * A217790 A217791 A217792 KEYWORD nonn,easy,base AUTHOR Michel Marcus, Mar 25 2013 STATUS approved

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Last modified October 19 03:08 EDT 2019. Contains 328211 sequences. (Running on oeis4.)