A257730 Permutation of natural numbers: a(1)=1; a(oddprime(n)) = prime(a(n)), a(not_an_oddprime(n)) = composite(a(n-1)).

1, 4, 2, 9, 7, 6, 3, 16, 14, 12, 23, 8, 17, 26, 24, 21, 13, 35, 5, 15, 27, 39, 53, 36, 33, 22, 51, 10, 43, 25, 37, 40, 56, 75, 52, 49, 83, 34, 72, 18, 19, 62, 59, 38, 54, 57, 101, 78, 102, 74, 69, 114, 89, 50, 98, 28, 30, 86, 73, 82, 41, 55, 76, 80, 134, 106, 149, 135, 100, 94, 11, 150, 47, 120, 70, 130, 42, 45, 103, 117, 99, 112, 167, 58, 77

Offset

1,2

Comments

Here composite(n) = n-th composite = A002808(n), prime(n) = n-th prime = A000040(n), oddprime(n) = n-th odd prime = A065091(n) = A000040(n+1), not_an_oddprime(n) = n-th natural number which is not an odd prime = A065090(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1; if A000035(n) = 1 and A010051(n) = 1 [i.e., when n is an odd prime], then a(n) = A000040(a(A000720(n)-1)), otherwise a(n) = A002808(a(A062298(n))). [Here A062298(n) gives the index of n among numbers larger than 1 which are not odd primes, 1 for 2, 2 for 4, 3 for 6, etc.]

As a composition of other permutations:

a(n) = A246378(A257727(n)).

a(n) = A257732(A257801(n)).

Prog

(Scheme, with memoizing definec-macro)
(definec (A257730 n) (cond ((<= n 1) n) ((and (odd? n) (= 1 (A010051 n))) (A000040 (A257730 (+ -1 (A000720 n))))) (else (A002808 (A257730 (A062298 n))))))
;; Alternatively, by composing other permutations:
(define (A257730 n) (A246378 (A257727 n)))

Crossrefs

Inverse: A257729.

Cf. A000040, A000720, A002808, A010051, A062298, A065090, A065091.

Related or similar permutations: A246378, A257727, A257732, A257801, A236854.

Sequence in context: A351164 A101690 A213781 * A246378 A260422 A237126

Adjacent sequences: A257727 A257728 A257729 * A257731 A257732 A257733

Keyword

nonn

Author

Antti Karttunen, May 09 2015

Status

approved