login
a(1) = 1; a(n) = smallest palindromic number of the form k*a(n-1) + 1 with k > 1.
6

%I #11 Jun 29 2023 18:06:11

%S 1,3,7,22,111,1111,11111,111111,1111111,11111111,111111111,1111111111,

%T 11111111111,111111111111,1111111111111,11111111111111,

%U 111111111111111,1111111111111111,11111111111111111,111111111111111111

%N a(1) = 1; a(n) = smallest palindromic number of the form k*a(n-1) + 1 with k > 1.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11, -10).

%F a(n) = (10^(n-2) - 1)/9 for n > 4.

%F G.f.: (110*x^5 - 61*x^4 - 25*x^3 - 16*x^2 - 8*x + 1)/(10*x-1)/(x-1). - Maksym Voznyy (voznyy(AT)mail.ru), Jan 10 2008

%p A069505:=seriestolist(taylor((1+110*x^5-61*x^4-25*x^3-16*x^2-8*x)/(10*x-1)/(x-1),x,20)); # Maksym Voznyy (voznyy(AT)mail.ru), Jan 10 2008

%Y Cf. A069506, A069507, A069508, A069509, A069510.

%K nonn,base

%O 0,2

%A _Amarnath Murthy_, Mar 30 2002

%E More terms from _Patrick De Geest_, Jun 11 2003