A377192 - OEIS

%I #22 Nov 11 2024 02:21:19

%S 0,10,1010,100110,10001110,1000011110,100000111110,10000001111110,

%T 1000000011111110,100000000111111110,10000000001111111110,

%U 1000000000011111111110,100000000000111111111110,10000000000001111111111110,1000000000000011111111111110,100000000000000111111111111110

%N Smallest number with the property that you have to change at least n digits to get a palindrome.

%C Positions of records in A377191.

%H Paolo Xausa, <a href="/A377192/b377192.txt">Table of n, a(n) for n = 0..450</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F a(n) = 10^(2*n-1) + (10^n-1)/9 - 1 for n > 0.

%F From _Stefano Spezia_, Oct 20 2024: (Start)

%F G.f.: 10*x*(1 - 10*x - 90*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).

%F E.g.f.: (81 - 100*exp(x) + 10*exp(10*x) + 9*exp(100*x))/90. (End)

%F a(n) = A007088(A143960(n)) for n > 0. - _Rémy Sigrist_, Nov 05 2024

%e 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.

%t A377192[n_] := Ceiling[10^(2*n-1) + (10^n-1)/9 - 1]; Array[A377192, 20, 0] (* or *)

%t LinearRecurrence[{111, -1110, 1000}, {0, 10, 1010, 100110}, 20] (* _Paolo Xausa_, Nov 06 2024 *)

%Y Cf. A002113, A007088, A143960, A377191.

%K nonn,base,easy

%O 0,2

%A _Franz Vrabec_, Oct 19 2024