A257690 Permutation of natural numbers: a(1) = 1, a(lucky(n)) = (2*a(n))-1, a(unlucky(n)) = 2*n, where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505.

1, 2, 3, 4, 6, 8, 5, 12, 7, 16, 10, 24, 11, 14, 15, 32, 20, 48, 22, 28, 9, 30, 64, 40, 23, 96, 44, 56, 18, 60, 13, 128, 31, 80, 46, 192, 19, 88, 112, 36, 120, 26, 47, 256, 62, 160, 92, 384, 21, 38, 27, 176, 224, 72, 240, 52, 94, 512, 124, 320, 184, 768, 29, 42, 76, 54, 63, 352, 39, 448, 144, 480, 95, 104, 43, 188, 1024, 248, 55

Offset

1,2

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; for n > 1: if A145649(n) = 1 [i.e., if n is lucky], then a(n) = (2*a(A109497(n)))-1, otherwise a(n) = 2*a(n-A109497(n)). [Where A109497(n) gives the number of lucky numbers <= n.]

Prog

(Scheme, with memoizing definec-macro)
(definec (A257690 n) (cond ((= 1 n) n) ((= 1 (A145649 n)) (+ -1 (* 2 (A257690 (A109497 n))))) (else (* 2 (A257690 (- n (A109497 n)))))))

Crossrefs

Inverse permutation: A183089.

Cf. A005408, A005843, A000959, A050505, A109497, A145649.

Cf. also A257725 (similar permutation with a slightly different definition, resulting the first differing term at n=13, where a(13) = 11, while A257725(13) = 9).

Cf. also A257735 - A257738.

Sequence in context: A038150 A182831 A257725 * A336322 A277519 A277623

Adjacent sequences: A257687 A257688 A257689 * A257691 A257692 A257693

Keyword

nonn

Author

Antti Karttunen, May 09 2015

Status

approved