A083816 10^n-th palindrome.

1, 11, 919, 90109, 9001009, 900010009, 90000100009, 9000001000009, 900000010000009, 90000000100000009, 9000000001000000009, 900000000010000000009, 90000000000100000000009, 9000000000001000000000009, 900000000000010000000000009, 90000000000000100000000000009, 9000000000000001000000000000009

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

From Chai Wah Wu, Jun 13 2024: (Start)

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 4.

G.f.: (-8000*x^4 + 690*x^3 - 808*x^2 + 100*x - 1)/((x - 1)*(10*x - 1)*(100*x - 1)). (End)

Mathematica

NextPalindrome[n_] := Block[{l = Floor[Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]]]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[Reverse[ IntegerDigits[idfhn]], Mod[l, 2]]]] ]]]]; p = NestList[ NextPalindrome, 1, 10^5]; Table[ p[[10^n]], {n, 0, 5}]

Crossrefs

Cf. A050250, A099280.

Cf. A103404.

Sequence in context: A052071 A176709 A336800 * A233092 A302374 A243818

Adjacent sequences: A083813 A083814 A083815 * A083817 A083818 A083819

Keyword

nonn,base

Author

Robert G. Wilson v, Jun 17 2003

Extensions

More terms from Ray Chandler, Jul 23 2003

Status

approved