A250250 Permutation of natural numbers: a(1) = 1, a(n) = A246278(a(A055396(n)),a(A078898(n))).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 22, 23, 24, 25, 26, 21, 28, 29, 30, 31, 32, 45, 34, 35, 36, 37, 38, 33, 40, 41, 54, 43, 44, 81, 46, 47, 48, 49, 50, 75, 52, 53, 42, 125, 56, 63, 58, 59, 60, 61, 62, 39, 64, 55, 90, 67, 68, 135, 70, 71, 72, 103, 74, 51, 76, 77, 66, 79, 80, 99, 82, 83

Offset: 1

Author

Antti Karttunen, Nov 17 2014

Keywords

• nonn

Comments

This is a "doubly-recursed" version of A249818.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3432
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A250249.

Fixed points: A250251, their complement: A249729.

Cf. A000035, A000040, A055396, A078442, A078898, A049076, A246278.

See also other (somewhat) similar permutations: A245821, A057505.

Differs from the "vanilla version" A249818 for the first time at n=42, where a(42) = 54, while A249818(42) = 42.

Formula

a(1) = 1, a(n) = A246278(a(A055396(n)), a(A078898(n))).

Other identities. For all n >= 1:

a(2n) = 2*a(n), or equally, a(n) = a(2n)/2. [The even bisection halved gives the sequence back].

a(p_n) = p_{a(n)}, or equally, a(n) = A049084(a(A000040(n))). [Restriction to primes induces the same sequence].

A078442(a(n)) = A078442(n), A049076(a(n)) = A049076(n). [Preserves the "order of primeness of n"].

A000035(n) = A000035(a(n)). [Preserves the parity].