A276441 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = 1 + 2*a(n), a(A088359(n)) = 2*a(n), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 8, 13, 10, 9, 11, 31, 30, 28, 24, 16, 29, 26, 20, 25, 18, 17, 27, 22, 21, 19, 23, 63, 62, 60, 56, 48, 32, 61, 58, 52, 40, 57, 50, 36, 49, 34, 33, 59, 54, 44, 53, 42, 41, 51, 38, 37, 35, 55, 46, 45, 43, 39, 47, 127, 126, 124, 120, 112, 96, 64, 125, 122, 116, 104, 80, 121, 114, 100, 72, 113, 98

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.

Index entries for sequences related to binary expansion of n

Index entries for Hofstadter-type sequences

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 1 + 2*a(A080677(n)-1), otherwise [when n is in A088359], a(n) = 2*a(A004001(n)-1).

As a composition of other permutations:

a(n) = A054429(A267111(n)).

a(n) = A233277(A276343(n)).

a(n) = A233275(A276345(n)).

a(n) = A006068(A276443(n)).

Other identities. For all n >= 1:

a(A000079(n-1)) = A000225(n).

Prog

(Scheme)
(definec (A276441 n) (cond ((< n 2) n) ((zero? (A093879 (- n 1))) (+ 1 (* 2 (A276441 (+ -1 (A080677 n)))))) (else (* 2 (A276441 (+ -1 (A004001 n)))))))

Crossrefs

Inverse: A276442.

Cf. A000079, A000225, A004001, A080677, A087686, A088359, A093879.

Related or similar permutations: A006068, A054429, A233275, A233277, A267111, A276343, A276345, A276443.

Cf. also arrays A265901, A265903.

Sequence in context: A335536 A233276 A304083 * A153141 A006068 A154436

Adjacent sequences: A276438 A276439 A276440 * A276442 A276443 A276444

Keyword

nonn,base

Author

Antti Karttunen, Sep 03 2016

Status

approved