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 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]. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 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]. PROG (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))))))) CROSSREFS Inverse: A246376. Similar or related permutations: A005940, A005941, A163511, A245606, A246378, A246379. Cf. A000035, A003961, A005408, A005843. Sequence in context: A269838 A246376 A269866 * A269865 A269387 A207801 Adjacent sequences:  A246372 A246373 A246374 * A246376 A246377 A246378 KEYWORD nonn AUTHOR Antti Karttunen, Aug 27 2014 STATUS approved

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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)