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

Author

Michel Marcus, Mar 25 2013

Keywords

• nonn
• easy
• base

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]

Examples

			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).
		

Links

• Cédric Villani, Les défis mathématiques du Monde, épisode 1 : les palindromes
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A050683, A070252.

Programs

PARI

A217789(n)=11-(n==3)-(n==1)*10  \\ [M. F. Hasler, Mar 25 2013]

Formula

G.f.: x*(1+10*x-x^2+x^3)/(1-x). [Bruno Berselli, Mar 25 2013]