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

1,2

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

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.]

Prog

(Scheme, with memoization-macro definec)
(definec (A267111 n) (cond ((< n 2) n) ((zero? (A093879 (- n 1))) (* 2 (A267111 (+ -1 (A080677 n))))) (else (+ 1 (* 2 (A267111 (+ -1 (A004001 n))))))))

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.

Sequence in context: A233280 A233279 A359752 * A161919 A269391 A095903

Adjacent sequences: A267108 A267109 A267110 * A267112 A267113 A267114

Keyword

nonn,look

Author

Antti Karttunen, Jan 10 2016

Status

approved