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

Author

Antti Karttunen, Aug 11 2016

Keywords

• nonn

Examples

			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.
		

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

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).

Programs

Scheme

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

Formula

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

Other identities:

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

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