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a(1) = 1; a(n) = smallest palindrome of the form k*a(n-1) + 1.
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%I #9 Jun 29 2023 18:10:42

%S 1,2,3,4,5,6,7,8,9,55,111,1111,11111,111111,1111111,11111111,

%T 111111111,1111111111,11111111111,111111111111,1111111111111,

%U 11111111111111,111111111111111,1111111111111111,11111111111111111,111111111111111111

%N a(1) = 1; a(n) = smallest palindrome of the form k*a(n-1) + 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 - 8) - 1}/9 for n >10.

%F From _Chai Wah Wu_, Jun 20 2016: (Start)

%F a(n) = 11*a(n-1) - 10*a(n-2) for n > 12.

%F G.f.: x*(440*x^11 - 404*x^10 + 36*x^9 - 9*x^8 - 9*x^7 - 9*x^6 - 9*x^5 - 9*x^4 - 9*x^3 - 9*x^2 - 9*x + 1)/((x - 1)*(10*x - 1)). (End)

%t a[1] = 1; a[n_] := a[n] = Block[{k = 1}, While[ FromDigits[ Reverse[ IntegerDigits[ k*a[n - 1] + 1]]] != k*a[n - 1] + 1, k++ ]; k*a[n - 1] + 1]; Table[ a[n], {n, 1, 26}]

%Y Cf. A069505, A069506, A069507, A069508, A069509.

%K nonn,base

%O 1,2

%A _Amarnath Murthy_, Mar 30 2002

%E Edited and extended by _Robert G. Wilson v_, Apr 19 2003