cp's OEIS Frontend

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

%I A275832 #18 Jun 24 2017 12:03:56
%S A275832 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,
%T A275832 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,
%U A275832 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
%N A275832 Size of the cycle containing element 1 in finite permutations listed in tables A060117 & A060118: a(n) = A007814(A275725(n)).
%H A275832 Antti Karttunen, <a href="/A275832/b275832.txt">Table of n, a(n) for n = 0..40320</a>
%H A275832 Indranil Ghosh, <a href="/A275832/a275832_1.txt">Python program for computing this sequence</a>
%H A275832 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A275832 a(n) = A007814(A275725(n)).
%F A275832 Other identities:
%F A275832 For n >= 1, a(A033312(n)) = n.
%F A275832 For n >= 2, a(A000142(n)) = 1.
%e A275832 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.
%e A275832 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.
%e A275832 For n=3, the permutation with rank 3 in list A060118 is "231" where 1 is in a 3-cycle, thus a(3)=3.
%e A275832 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.
%e A275832 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.
%o A275832 (Scheme) (define (A275832 n) (A007814 (A275725 n)))
%Y A275832 Cf. A060117, A060118.
%Y A275832 Cf. A000142, A007814, A033312, A275725, A275807.
%Y A275832 Cf. A153880 (positions of 1's), A273670 (of terms larger than one), A275833 (of odd terms), A275834 (of even terms).
%K A275832 nonn
%O A275832 0,2
%A A275832 _Antti Karttunen_, Aug 11 2016