# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a245613 Showing 1-1 of 1 %I A245613 #23 Jan 09 2024 12:31:57 %S A245613 1,2,4,3,8,6,5,16,9,7,11,10,32,18,13,12,17,15,22,20,35,19,66,14,24,21, %T A245613 34,25,23,33,31,45,63,37,27,26,41,36,29,43,69,40,134,30,47,39,44,68, %U A245613 71,50,38,46,67,131,28,49,42,70,64,52,92,48,127,65,61,75,55,51,89,83,73,60 %N A245613 Permutation of natural numbers: a(1) = 1; thereafter, if n is k-th number with an odd number of prime divisors (counted with multiplicity) [i.e., n = A026424(k)], a(n) = A244991(a(k)), otherwise, when n is k-th number > 1 with an even number of prime divisors [i.e., n = A028260(1+k)], a(n) = A244990(1+a(k)). %C A245613 This shares with the permutation A122111 the property that each term of A028260 is mapped to a unique term of A244990 and each term of A026424 is mapped to a unique term of A244991. %H A245613 Antti Karttunen, Table of n, a(n) for n = 1..10001 %H A245613 Index entries for sequences that are permutations of the natural numbers %F A245613 a(1) = 1, and for n > 1, if A066829(n) = 1, a(n) = A244991(a(A055038(n))), otherwise a(n) = A244990(1+a(A055037(n)-1)). %F A245613 As a composition of related permutations: %F A245613 a(n) = A244322(A245603(n)). %F A245613 For all n >= 1, A066829(n) = A244992(a(n)). %o A245613 (Scheme, with memoization macro definec) %o A245613 (definec (A245613 n) (cond ((= 1 n) 1) ((= 1 (A066829 n)) (A244991 (A245613 (A055038 n)))) (else (A244990 (+ 1 (A245613 (-1+ (A055037 n)))))))) %Y A245613 Inverse: A245614. %Y A245613 Cf. A026424, A028260, A055037, A055038, A066829, A244990, A244991, A244992, A122111. %Y A245613 Similar entanglement permutations: A243287, A243343, A243345, A244321-A244322, A245603, A135141, A237427, A245605. %K A245613 nonn %O A245613 1,2 %A A245613 _Antti Karttunen_, Jul 27 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE