|
%I #13 Sep 01 2014 11:46:54
%S 1,2,3,4,5,6,9,8,7,10,15,12,11,18,21,16,25,14,27,20,13,30,81,24,17,22,
%T 45,36,23,42,39,32,19,50,51,28,35,54,99,40,55,26,33,60,37,162,129,48,
%U 49,34,75,44,29,90,87,72,41,46,135,84,47,78,189,64,65,38,63,100,95,102,153,56,31,70
%N Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A003961(1+a(n)). [Where A003961(n) shifts the prime factorization of n one step towards larger primes].
%C This can be viewed as yet another "entanglement permutation" where the two complementary pairs to be interwoven together are even and odd numbers (A005843/A005408) which are entangled with the complementary pair even numbers (taken straight) and odd numbers in the order they appear in A003961: (A005843/A003961). Sequence A163511 has almost the same definition, but its domain starts from 0, which results a different permutation.
%H Antti Karttunen, <a href="/A246375/b246375.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A003961(1+a(n)). [Where A003961(n) shifts the prime factorization of n one step towards larger primes].
%F As a composition of related permutations:
%F a(n) = A246379(A246378(n)).
%F Other identities. For all n >= 1 the following holds:
%F A000035(a(n)) = A000035(n). [Like A005940 & A005941, this also preserves the parity].
%o (PARI)
%o default(primelimit, (2^31)+(2^30));
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of _Michel Marcus_
%o A246375(n) = if(1==n, 1, if(!(n%2), 2*A246375(n/2), A003961(1+A246375((n-1)/2))));
%o for(n=1, 16384, write("b246375.txt", n, " ", A246375(n)));
%o (Scheme, with memoizing definec-macro)
%o (definec (A246375 n) (cond ((<= n 1) n) ((even? n) (* 2 (A246375 (/ n 2)))) (else (A003961 (+ 1 (A246375 (/ (- n 1) 2)))))))
%Y Inverse: A246376.
%Y Similar or related permutations: A005940, A005941, A163511, A245606, A246378, A246379.
%Y Cf. A000035, A003961, A005408, A005843.
%K nonn
%O 1,2
%A _Antti Karttunen_, Aug 27 2014
|
