A377192 Smallest number with the property that you have to change at least n digits to get a palindrome.
0, 10, 1010, 100110, 10001110, 1000011110, 100000111110, 10000001111110, 1000000011111110, 100000000111111110, 10000000001111111110, 1000000000011111111110, 100000000000111111111110, 10000000000001111111111110, 1000000000000011111111111110, 100000000000000111111111111110
Offset: 0
Examples
a(2) = 1010 because 1010 is the smallest number with the property that you have to change at least 2 digits to get a palindrome.
Links
- Paolo Xausa, Table of n, a(n) for n = 0..450
- Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
Programs
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Mathematica
A377192[n_] := Ceiling[10^(2*n-1) + (10^n-1)/9 - 1]; Array[A377192, 20, 0] (* or *) LinearRecurrence[{111, -1110, 1000}, {0, 10, 1010, 100110}, 20] (* Paolo Xausa, Nov 06 2024 *)
Formula
a(n) = 10^(2*n-1) + (10^n-1)/9 - 1 for n > 0.
From Stefano Spezia, Oct 20 2024: (Start)
G.f.: 10*x*(1 - 10*x - 90*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
E.g.f.: (81 - 100*exp(x) + 10*exp(10*x) + 9*exp(100*x))/90. (End)
Comments