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A246380 Permutation of natural numbers: a(1) = 1, a(2n) = nthcomposite(a(n)), a(2n-1) = nthprime(a(A064989(2n-1)-1)), where nthprime = A000040, nthcomposite = A002808, and A064989(n) shifts the prime factorization of n one step towards smaller primes. 6
1, 4, 2, 9, 7, 6, 23, 16, 3, 14, 13, 12, 43, 35, 17, 26, 37, 8, 101, 24, 5, 22, 19, 21, 53, 62, 83, 51, 79, 27, 233, 39, 191, 54, 149, 15, 103, 134, 11, 36, 47, 10, 151, 34, 41, 30, 29, 33, 73, 75, 241, 86, 113, 114, 89, 72, 1153, 108, 443, 40, 593, 296, 547, 56, 167, 245, 173, 76, 563, 194, 1553, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Has an infinite number of infinite cycles. See comments in A246379.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..3098

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1, a(2n) = nthcomposite(a(n)), a(2n-1) = nthprime(a(A064989(2n-1)-1)), where nthprime = A000040, nthcomposite = A002808, and A064989(n) shifts the prime factorization of n one step towards smaller primes.

As a composition of related permutations:

a(n) = A246378(A246376(n)).

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

A010051(a(n)) = A000035(n). [Maps odd numbers larger than one to primes, and even numbers to composites, in some order. Permutations A246378 & A246682 have the same property].

PROG

(PARI)

default(primelimit, (2^31)+(2^30));

A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n }; \\ This function from M. F. Hasler

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A246380(n) = if(1==n, 1, if(!(n%2), A002808(A246380(n/2)), prime(A246380(A064989(n)-1))));

for(n=1, 3098, write("b246380.txt", n, " ", A246380(n)));

(Scheme, with memoization-macro definec)

(definec (A246380 n) (cond ((< n 2) n) ((even? n) (A002808 (A246380 (/ n 2)))) (else (A000040 (A246380 (- (A064989 n) 1))))))

CROSSREFS

Inverse: A246379.

Similar or related permutations: A246376, A246378, A246363, A246364, A246366, A246368, A064216, A246682.

Cf. A000035, A000040, A002808, A010051, A064989.

Sequence in context: A246378 A260422 A237126 * A200639 A243968 A104583

Adjacent sequences:  A246377 A246378 A246379 * A246381 A246382 A246383

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 29 2014

STATUS

approved

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Last modified February 20 08:44 EST 2019. Contains 320325 sequences. (Running on oeis4.)