A269858 Permutation of natural numbers: a(1) = 1, a(2n) = A065090(1+a(n)), a(2n+1) = A000040(a(A268674(2n+1))).

1, 2, 3, 4, 5, 6, 11, 8, 7, 9, 31, 10, 127, 18, 13, 14, 709, 12, 5381, 15, 19, 45, 52711, 16, 17, 165, 23, 27, 648391, 21, 9737333, 22, 29, 856, 41, 20, 174440041, 6185, 61, 24, 3657500101, 28, 88362852307, 63, 43, 58644, 2428095424619, 25, 59, 26, 37, 212, 75063692618249, 34, 67, 39, 47

Offset

1,2

Comments

Terms for prime positions copied from A007097.

Links

Table of n, a(n) for n=1..57.

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2) = 2, for n > 2, if n is even, a(n) = A002808(a(n/2)-1), and for odd n, a(n) = A000040(a(A268674(n))).

As a composition of other permutations:

a(n) = A237739(A252756(n)).

Other identities. For all n >= 1:

a(A000040(n)) = A007097(n). [Maps primes to the primeth recurrence.]

Prog

(Scheme, with memoization-macro definec)
(definec (A269858 n) (cond ((<= n 1) n) ((even? n) (A065090 (+ 1 (A269858 (/ n 2))))) (else (A000040 (A269858 (A268674 n))))))

Crossrefs

Inverse: A269857.

Cf. A000040, A007097, A065090, A268674.

Related or similar permutations: A237739, A252756, A269848.

Sequence in context: A270890 A010350 A306581 * A269848 A245706 A072622

Adjacent sequences: A269855 A269856 A269857 * A269859 A269860 A269861

Keyword

nonn

Author

Antti Karttunen, Mar 06 2016

Status

approved