A257725 - OEIS

A257725

Permutation of natural numbers: a(0) = 0, a(lucky(n)) = 1 + 2*a(n-1), a(unlucky(n)) = 2*a(n), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505.

0, 1, 2, 3, 4, 6, 8, 5, 12, 7, 16, 10, 24, 9, 14, 13, 32, 20, 48, 18, 28, 17, 26, 64, 40, 11, 96, 36, 56, 34, 52, 25, 128, 15, 80, 22, 192, 33, 72, 112, 68, 104, 50, 21, 256, 30, 160, 44, 384, 49, 66, 19, 144, 224, 136, 208, 100, 42, 512, 60, 320, 88, 768, 29, 98, 132, 38, 27, 288, 65, 448, 272, 416, 41, 200, 97, 84, 1024, 120, 37

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OFFSET

0,3

COMMENTS

In other words, after a(0) = 0, if n is the k-th lucky number [i.e., n = A000959(k)], a(n) = 1 + 2*a(k-1); otherwise, when n is the k-th unlucky number [i.e., n = A050505(k)], a(n) = 2*a(k).

Because all lucky numbers are odd, it means that odd numbers occur in odd positions only (together with some even numbers, for each one of which there is a separate infinite cycle), while the even positions contain only even numbers.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(0) = 0; for n >= 1: if A145649(n) = 1 [i.e., if n is lucky], then a(n) = 1+(2*a(A109497(n)-1)), otherwise a(n) = 2*a(n-A109497(n)). [Where A109497(n) gives the number of lucky numbers <= n.]

As a composition of other permutations. For all n >= 1:

a(n) = A246377(A257732(n)).

a(n) = A237427(A257734(n)).

PROG

(Scheme, with memoizing definec-macro)

(definec (A257725 n) (cond ((zero? n) n) ((= 1 (A145649 n)) (+ 1 (* 2 (A257725 (- (A109497 n) 1))))) (else (* 2 (A257725 (- n (A109497 n)))))))

CROSSREFS

Inverse: A257726.

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

Related or similar permutations: A237427, A246377, A257732, A257734.

Cf. also A257690 (another similar permutation, but with a slightly different definition, resulting the first differing term at n=13, where a(13) = 9, while A257690(13) = 11).

Cf. also A257735 - A257738.

Sequence in context: A225850 A038150 A182831 * A257690 A336322 A277519

Adjacent sequences: A257722 A257723 A257724 * A257726 A257727 A257728

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 06 2015

EXTENSIONS

Formula in name corrected by Antti Karttunen, Jan 10 2016

STATUS

approved