A246378 Permutation of natural numbers: a(1) = 1, a(2n) = nthcomposite(a(n)), a(2n+1) = nthprime(a(n)), where nthcomposite = A002808, nthprime = A000040.

1, 4, 2, 9, 7, 6, 3, 16, 23, 14, 17, 12, 13, 8, 5, 26, 53, 35, 83, 24, 43, 27, 59, 21, 37, 22, 41, 15, 19, 10, 11, 39, 101, 75, 241, 51, 149, 114, 431, 36, 89, 62, 191, 40, 103, 82, 277, 33, 73, 54, 157, 34, 79, 58, 179, 25, 47, 30, 67, 18, 29, 20, 31, 56, 167, 134, 547, 102, 379, 304, 1523, 72, 233

Offset: 1

Author

Antti Karttunen, Aug 27 2014

Keywords

• nonn
• look

Comments

Contains an infinite number of infinite cycles. See comments at A246377.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A246377.

Similar or related permutations: A237126, A054429, A227413, A236854, A246375, A246380, A246682, A163511.

Cf. A000035, A000040, A002808, A010051, A071904.

Programs

PARI

A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n }; \\ This function from M. F. Hasler
A246378(n) = if(1==n, 1, if(!(n%2), A002808(A246378(n/2)), prime(A246378((n-1)/2))));
for(n=1, 4096, write("b246378.txt", n, " ", A246378(n)));
(Scheme, with memoizing definec-macro)
(definec (A246378 n) (cond ((< n 2) n) ((even? n) (A002808 (A246378 (/ n 2)))) (else (A000040 (A246378 (/ (- n 1) 2))))))

Formula

a(1) = 1, a(2n) = nthcomposite(a(n)), a(2n+1) = nthprime(a(n)), where nthcomposite = A002808, nthprime = A000040.

As a composition of related permutations:

a(n) = A227413(A054429(n)).

a(n) = A236854(A227413(n)).

a(n) = A246380(A246375(n)).

a(n) = A246682(A163511(n)). [For n >= 1].

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 A246380 & A246682 have the same property].