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

0,1

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).

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)

a(n) ~ n. - Charles R Greathouse IV, May 30 2026

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 *)

Prog

(PARI) a(n)=if(n>19, n+(-1)^n, [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9][n+1]) \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A004442.

Sequence in context: A303879 A305947 A100830 * A377712 A350494 A168100

Adjacent sequences: A180173 A180174 A180175 * A180177 A180178 A180179

Keyword

base,nonn,easy,changed

Author

Reinhard Zumkeller, Aug 15 2010

Status

approved