A104459 - OEIS

%I #21 Dec 10 2021 11:27:30

%S 1,2,10,11,100,110,1000,1100,10000,11000,100000,110000,1000000,

%T 1100000,10000000,11000000,100000000,110000000,1000000000,1100000000,

%U 10000000000,11000000000,100000000000,110000000000,1000000000000,1100000000000,10000000000000

%N Possible differences between adjacent palindromes.

%C Possible first differences of A002113.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,10).

%F a(n) = 2 if n = 2; 11*10^((n-4)/2) if n even >= 4; 10^((n-1)/2) if n odd.

%F a(n) = 10*a(n-2), starting 1,2,10,11.

%F G.f.: x*(1 + 2*x - 9*x^3)/(1 - 10*x^2). - _Stefano Spezia_, Dec 08 2021

%e 536635 and 537735 are adjacent palindromes, so 537735-536635 = 1100 is in the sequence.

%t PalindromeQ[n_]:=Reverse[IntegerDigits[n]]==IntegerDigits[n];q=0;lst={};Do[If[PalindromeQ[n],AppendTo[lst,n-q];q=n],{n,10!}];Union@lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 26 2009 *)

%t Flatten[Join[{1,2},Table[{10,11}10^n,{n,0,15}]]] (* _Harvey P. Dale_, Dec 22 2012 *)

%Y Cf. A002113.

%K base,easy,nonn

%O 1,2

%A _David W. Wilson_, Mar 08 2005