A275832 Size of the cycle containing element 1 in finite permutations listed in tables A060117 & A060118: a(n) = A007814(A275725(n)).

1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 4, 1, 3, 1, 4, 2, 4, 2, 3, 2, 4, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2, 1, 5, 4, 5, 1, 4, 1, 5, 2, 5, 3, 4, 3, 5, 4, 5, 1, 2, 1, 4, 3, 4, 1, 2, 1, 5, 4, 5, 1, 3, 1, 5, 3, 5, 2, 3, 2, 5, 4, 5, 1, 3, 1, 4, 2, 4, 1, 3, 1, 5, 3, 5, 1, 4, 1, 5, 2, 5, 2, 4, 2, 5, 3, 5, 2, 3, 2, 4, 3, 4, 2, 3, 2, 5, 4, 5, 2, 4, 2, 5, 3, 5, 3, 4, 3, 5, 4, 5, 1

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Indranil Ghosh, Python program for computing this sequence

Index entries for sequences related to factorial base representation

Formula

a(n) = A007814(A275725(n)).

Other identities:

For n >= 1, a(A033312(n)) = n.

For n >= 2, a(A000142(n)) = 1.

Example

For n=0, the permutation with rank 0 in list A060118 is "1" (identity permutation) where 1 is fixed (in a 1-cycle), thus a(0)=1.
For n=1, the permutation with rank 1 in list A060118 is "21" where 1 is in a transposition (a 2-cycle), thus a(1)=2.
For n=3, the permutation with rank 3 in list A060118 is "231" where 1 is in a 3-cycle, thus a(3)=3.
For n=16, the permutation with rank 16 in list A060118 is "3412" (1 is in the other of two disjoint transpositions (1 3) and (2 4)), thus a(16)=2.
For n=44, the permutation with rank 44 in list A060118 is "43251", where 1 is a part of 3-cycle, thus a(44)=3.

Prog

(Scheme) (define (A275832 n) (A007814 (A275725 n)))

Crossrefs

Cf. A060117, A060118.

Cf. A000142, A007814, A033312, A275725, A275807.

Cf. A153880 (positions of 1's), A273670 (of terms larger than one), A275833 (of odd terms), A275834 (of even terms).

Sequence in context: A005679 A232927 A350651 * A237839 A101608 A102853

Adjacent sequences: A275829 A275830 A275831 * A275833 A275834 A275835

Keyword

nonn

Author

Antti Karttunen, Aug 11 2016

Status

approved