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

Author

Antti Karttunen, Sep 03 2016

Keywords

• nonn
• base

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

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.

Programs

Scheme

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

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).