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

1,2

Comments

Possible first differences of A002113.

Links

Table of n, a(n) for n=1..27.

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

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

Example

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

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 *)

Crossrefs

Cf. A002113.

Sequence in context: A023151 A342535 A265747 * A008560 A188283 A174703

Adjacent sequences: A104456 A104457 A104458 * A104460 A104461 A104462

Keyword

base,easy,nonn

Author

David W. Wilson, Mar 08 2005

Status

approved