A267111 Permutation of natural numbers: a(1) = 1, a(A087686(n)) = 2*a(n-1), a(A088359(n)) = 1+2*a(n), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001, the Hofstadter-Conway $10000 sequence.

1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 15, 10, 13, 14, 12, 16, 17, 19, 23, 31, 18, 21, 27, 22, 29, 30, 20, 25, 26, 28, 24, 32, 33, 35, 39, 47, 63, 34, 37, 43, 55, 38, 45, 59, 46, 61, 62, 36, 41, 51, 42, 53, 54, 44, 57, 58, 60, 40, 49, 50, 52, 56, 48, 64, 65, 67, 71, 79, 95, 127, 66, 69, 75, 87, 111, 70, 77, 91, 119, 78, 93, 123

Offset: 1

Author

Antti Karttunen, Jan 10 2016

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Antti Karttunen, Entanglement Permutations, 2016-2017
• T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
• Index entries for Hofstadter-type sequences
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A267112.

Cf. A004001, A080677, A087686, A088359, A093879, A267108, A267109.

Similar or related permutations: A006068, A054429, A276441, A233275, A233277, A276343, A276345, A276445.

Cf. also permutations A266411, A266412 and arrays A265901, A265903.

Formula

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

Equally, for n > 1, if A093879(n-1) = 0, a(n) = 2*a(n - A004001(n)), otherwise a(n) = 1 + 2*a(A004001(n)-1). [Above formula in a more symmetric form.]

As a composition of other permutations:

a(n) = A054429(A276441(n)).

a(n) = A233275(A276343(n)).

a(n) = A233277(A276345(n)).

a(n) = A006068(A276445(n)).

Other identities. For all n >= 0:

a(2^n) = 2^n. [Follows from the properties (3) and (4) of A004001 given on page 227 of Kubo & Vakil paper.]