A104459 Possible differences between adjacent palindromes.

1, 2, 10, 11, 100, 110, 1000, 1100, 10000, 11000, 100000, 110000, 1000000, 1100000, 10000000, 11000000, 100000000, 110000000, 1000000000, 1100000000, 10000000000, 11000000000, 100000000000, 110000000000, 1000000000000, 1100000000000, 10000000000000

Offset: 1

Author

David W. Wilson, Mar 08 2005

Keywords

• base
• easy
• nonn

Comments

Possible first differences of A002113.

Examples

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

Links

• Index entries for linear recurrences with constant coefficients, signature (0,10).

Crossrefs

Cf. A002113, A109868.

Programs

Mathematica

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

Formula

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

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

G.f.: x*(1 + 2*x - 9*x^3)/(1 - 10*x^2). - Stefano Spezia, Dec 08 2021