A217789 Least difference between 2 palindromic numbers of length n.

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

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

Table of n, a(n) for n=1..65.

Cédric Villani, Les défis mathématiques du Monde, épisode 1 : les palindromes

Index entries for linear recurrences with constant coefficients, signature (1).

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 * A347765 A004283 A344367

Adjacent sequences: A217786 A217787 A217788 * A217790 A217791 A217792

Keyword

nonn,easy,base

Author

Michel Marcus, Mar 25 2013

Status

approved