A246375 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].

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, 45, 36, 23, 42, 39, 32, 19, 50, 51, 28, 35, 54, 99, 40, 55, 26, 33, 60, 37, 162, 129, 48, 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

Offset: 1

Author

Antti Karttunen, Aug 27 2014

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A246376.

Similar or related permutations: A005940, A005941, A163511, A245606, A246378, A246379.

Cf. A000035, A003961, A005408, A005843.

Programs

PARI

default(primelimit, (2^31)+(2^30));
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
A246375(n) = if(1==n, 1, if(!(n%2), 2*A246375(n/2), A003961(1+A246375((n-1)/2))));
for(n=1, 16384, write("b246375.txt", n, " ", A246375(n)));
(Scheme, with memoizing definec-macro)
(definec (A246375 n) (cond ((<= n 1) n) ((even? n) (* 2 (A246375 (/ n 2)))) (else (A003961 (+ 1 (A246375 (/ (- n 1) 2)))))))

Formula

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].

As a composition of related permutations:

a(n) = A246379(A246378(n)).

Other identities. For all n >= 1 the following holds:

A000035(a(n)) = A000035(n). [Like A005940 & A005941, this also preserves the parity].