A180176 Lexicographically earliest permutation of the natural numbers such that a(n) != n and in decimal representation a(n) and n have at least one common digit.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48, 51, 50, 53, 52, 55, 54, 57, 56, 59, 58, 61, 60, 63, 62, 65, 64, 67, 66, 69, 68, 71, 70, 73

Offset: 0

Author

Reinhard Zumkeller, Aug 15 2010

Keywords

• base
• nonn

Comments

The permutation is self-inverse;

a(n) = A004442(n) for n >= 20.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for sequences that are permutations of the natural numbers
• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Programs

Mathematica

CoefficientList[Series[(-9 x^22 - 2 x^21 + 11 x^20 + 20 x^12 - 20 x^10 - 9 x^2 + x + 10) / ((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 23 2018 *)

Formula

From Chai Wah Wu, Oct 22 2018: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 22.

G.f.: (-9*x^22 - 2*x^21 + 11*x^20 + 20*x^12 - 20*x^10 - 9*x^2 + x + 10)/((x - 1)^2*(x + 1)). (End)