A256508 Lexicographically earliest sequence of distinct terms, with a unique fixed point, such that a^n(n)=n, for any n>0 (where a^n denotes the n-th iterate of a).

1, 4, 6, 2, 10, 9, 14, 12, 3, 15, 22, 8, 26, 21, 20, 18, 34, 16, 38, 25, 28, 33, 46, 27, 5, 39, 30, 35, 58, 24, 62, 36, 44, 51, 42, 32, 74, 57, 52, 45, 82, 49, 86, 55, 50, 69, 94, 54, 7, 60, 68, 65, 106, 48, 66, 63, 76, 87, 118, 70, 122, 93, 77, 72, 78, 88

Offset

1,2

Comments

The unique fixed point constraint ensures that this sequence differs from A000027.

This is a permutation of the natural numbers, with inverse A256513.

The length of the orbit of n is a prime divisor of n, for any n>1.

GCD(n, a(n))>1, for any n>1.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, Perl program for this sequence

Wikipedia, Iterated function

Index entries for sequences that are permutations of the natural numbers

Example

a^1(1)=a(1)=1.
a^2(2)=a(a(2))=a(4)=2.
a^3(3)=a(a(a(3)))=a(a(6))=a(9)=3.

Prog

(Perl) See Links section.

Crossrefs

Cf. A256513.

Sequence in context: A159193 A118967 A366952 * A059030 A066984 A364724

Adjacent sequences: A256505 A256506 A256507 * A256509 A256510 A256511

Keyword

nonn,nice

Author

Paul Tek, Mar 31 2015

Status

approved