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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
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]
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
Sequence in context: A059941 A086100 A182782 * A347765 A004283 A376165
KEYWORD
nonn,easy,base
AUTHOR
Michel Marcus, Mar 25 2013
STATUS
approved