A083816 - OEIS

%I #13 Jun 14 2024 04:12:28

%S 1,11,919,90109,9001009,900010009,90000100009,9000001000009,

%T 900000010000009,90000000100000009,9000000001000000009,

%U 900000000010000000009,90000000000100000000009,9000000000001000000000009,900000000000010000000000009,90000000000000100000000000009,9000000000000001000000000000009

%N 10^n-th palindrome.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F From _Chai Wah Wu_, Jun 13 2024: (Start)

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

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

%t 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}]

%Y Cf. A050250, A099280.

%Y Cf. A103404.

%K nonn,base

%O 0,2

%A _Robert G. Wilson v_, Jun 17 2003

%E More terms from _Ray Chandler_, Jul 23 2003