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A104459 Possible differences between adjacent palindromes. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 06:18 EST 2022. Contains 358431 sequences. (Running on oeis4.)