A250245 Permutation of natural numbers: a(1) = 1, a(n) = A083221(A055396(n),a(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, 54, 43, 44, 33, 46, 47, 48, 49, 50, 75, 52, 53, 42, 65, 56, 99, 58, 59, 60, 61, 62, 57, 64, 95, 78, 67, 68, 111, 70, 71, 72, 73, 74, 51, 76, 77, 126, 79, 80, 45, 82

Offset

1,2

Comments

The first 7-cycle occurs at: (33 39 63 57 99 81 45) which is mirrored by the cycle (66 78 126 114 198 162 90) with double-size terms.

The cycle which contains 55 as its smallest term, goes as: 55, 65, 95, 185, 425, 325, 205, 455, 395, 1055, 2945, 6035, 30845, ...

while to the other direction (A250246) it goes as: 55, 125, 245, 115, 625, 8575, 40375, ...

The cycle which contains 69 as its smallest term, goes as: 69, 111, 183, 351, 261, 273, 387, 489, 939, 1863, 909, 1161, 981, 1281, 4167, ...

while to the other direction (A250246) it goes as: 69, 135, 87, 105, 225, 207, 231, 195, 525, 1053, 3159, 24909, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

Formula

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

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A064989(2n+1))). - Antti Karttunen, Jan 18 2015

As a composition of related permutations:

a(n) = A252755(A243071(n)).

Other identities. For all n >= 1:

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

A020639(a(n)) = A020639(n) and A055396(a(n)) = A055396(n). [Preserves the smallest prime factor of n].

Prog

(Scheme, with memoizing-macro definec from Antti Karttunen's IntSeq-library, three alternative definitions)
(definec (A250245 n) (cond ((<= n 1) n) (else (A083221bi (A055396 n) (A250245 (A246277 n)))))) ;; Code for A083221bi given in A083221
(definec (A250245 n) (cond ((<= n 1) n) ((even? n) (* 2 (A250245 (/ n 2)))) (else (A250469 (A250245 (A064989 n))))))
(define (A250245 n) (A252755 (A243071 n)))

Crossrefs

Inverse: A250246.

Other similar permutations: A250244, A250247, A250249, A243071, A252755.

Cf. A005843, A020639, A055396, A064989, A083221, A246277, A250469.

Differs from the "vanilla version" A249817 for the first time at n=42, where a(42) = 54, while A249817(42) = 42.

Differs from A250246 for the first time at n = 33, where a(33) = 39, while A250246(33) = 45.

Differs from A250249 for the first time at n=73, where a(73) = 73, while A250249(73) = 103.

Sequence in context: A358140 A249817 A250247 * A250249 A249818 A250248

Adjacent sequences: A250242 A250243 A250244 * A250246 A250247 A250248

Keyword

nonn

Author

Antti Karttunen, Nov 17 2014

Status

approved