A069510 a(1) = 1; a(n) = smallest palindrome of the form k*a(n-1) + 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 55, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (11, -10).

Formula

a(n) = {10^(n - 8) - 1}/9 for n >10.

From Chai Wah Wu, Jun 20 2016: (Start)

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

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)

Mathematica

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}]

Crossrefs

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

Sequence in context: A122627 A122629 A083477 * A062388 A070244 A302500

Adjacent sequences: A069507 A069508 A069509 * A069511 A069512 A069513

Keyword

nonn,base

Author

Amarnath Murthy, Mar 30 2002

Extensions

Edited and extended by Robert G. Wilson v, Apr 19 2003

Status

approved