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.
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:
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
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Jan 10 2016
STATUS
approved