A109868 Numbers which can be differences of successive palindromes in order of their first occurrence.

1, 2, 11, 10, 110, 100, 1100, 1000, 11000, 10000, 110000, 100000, 1100000, 1000000, 11000000, 10000000, 110000000, 100000000, 1100000000, 1000000000, 11000000000, 10000000000, 110000000000, 100000000000, 1100000000000, 1000000000000, 11000000000000, 10000000000000

Offset

1,2

Comments

Except a(2)=2, all other terms contain digits 1 or 0.

Almost the same as A104459. - Georg Fischer, Apr 17 2025

Links

Table of n, a(n) for n=1..28.

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

Formula

From Elmo R. Oliveira, May 22 2026: (Start)

G.f.: x*(1 + 2*x + x^2 - 10*x^3)/(1 - 10*x^2).

a(n) = 10*a(n-2) for n > 4.

a(1)=1, a(2)=2; a(n) = 11*10^((n-3)/2) if n odd >= 3; a(n) = 10^((n/2)-1) if n even >= 4. (End)

Example

11 comes before 10 as 11 = 22-11 and 10 = 111-101, 11 occurs earlier to 10 as a successive palindrome difference.

Mathematica

LinearRecurrence[{0, 10}, {1, 2, 11, 10}, 50] (* Georg Fischer, Apr 17 2025 *)

Crossrefs

Cf. A104459.

Sequence in context: A163344 A064743 A376606 * A153521 A153650 A338049

Adjacent sequences: A109865 A109866 A109867 * A109869 A109870 A109871

Keyword

base,nonn,easy,changed

Author

Amarnath Murthy, Jul 09 2005

Extensions

More terms from Erich Friedman, Aug 08 2005

Offset changed by Andrew Howroyd, Sep 17 2024

More terms from Elmo R. Oliveira, May 22 2026

Status

approved