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

0,2

Comments

Positions of records in A377191.

Links

Paolo Xausa, Table of n, a(n) for n = 0..450

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

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)

a(n) = A007088(A143960(n)) for n > 0. - Rémy Sigrist, Nov 05 2024

Example

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.

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 *)

Crossrefs

Cf. A002113, A007088, A143960, A377191.

Sequence in context: A075171 A106456 A079214 * A163662 A176067 A080070

Adjacent sequences: A377189 A377190 A377191 * A377193 A377194 A377195

Keyword

nonn,base,easy

Author

Franz Vrabec, Oct 19 2024

Status

approved