A250247 Permutation of natural numbers: a(1) = 1, a(n) = A083221(a(A055396(n)),A246277(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, 39, 34, 35, 36, 37, 38, 63, 40, 41, 42, 43, 44, 33, 46, 47, 48, 49, 50, 75, 52, 53, 54, 65, 56, 99, 58, 59, 60, 61, 62, 57, 64, 95, 66, 67, 68, 111, 70, 71, 72, 103, 74, 51, 76, 77, 78, 79, 80, 45, 82

Offset

1,2

Comments

The first 7-cycle occurs at: (33 39 63 57 99 81 45), which is mirrored at the cycle (137 167 307 269 523 419 197), consisting of primes (p_33, p_39, p_63, ...).

Links

Antti Karttunen, Table of n, a(n) for n = 1..4240

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(n) = A083221(a(A055396(n)),A246277(n)).

Other identities. For all n >= 1:

a(A005843(n)) = A005843(n). [Fixes even numbers].

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"].

Example

As a(21) = 27, and A000040(21) = 73 and A000040(27) = 103, a(73) = 103.

Prog

(Scheme, with memoizing-macro definec from Antti Karttunen's IntSeq-library)
(definec (A250247 n) (cond ((<= n 1) n) (else (A083221bi (A250247 (A055396 n)) (A246277 n))))) ;; Code for A083221bi given in A083221

Crossrefs

Inverse: A250248.

Cf. A000040, A005843, A049076, A049084, A055396, A078442, A083221, A246277.

Differs from its inverse A250248 for the first time at n = 33, where a(33) = 39, while A250248(33) = 45.

Differs from the "vanilla version" A249817 for the first time at n=73, where a(73) = 103, while A249817(73) = 73.

Differs from "doubly recursed" version A250249 for the first time at n=42, where a(42) = 42, while A250249(42) = 54, thus the first prime where they get different values is p_42 = 181, where a(181) = 181, while A250249(181) = 251 = p_54.

Sequence in context: A272325 A358140 A249817 * A250245 A250249 A249818

Adjacent sequences: A250244 A250245 A250246 * A250248 A250249 A250250

Keyword

nonn

Author

Antti Karttunen, Nov 17 2014

Status

approved