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Permutation of natural numbers: a(1) = 1; a(A001969(1+n)) = A088359(a(n)), a(A000069(1+n)) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.
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%I #7 Sep 03 2016 17:04:59

%S 1,2,3,4,5,6,7,8,9,10,12,11,14,15,13,16,17,18,21,19,24,27,22,20,26,30,

%T 25,31,28,23,29,32,33,34,38,35,42,48,39,36,45,54,43,58,49,40,51,37,47,

%U 57,46,62,55,44,56,63,59,50,60,41,53,61,52,64,65,66,71,67,76,86,72,68,80,96,77,106,87,73,90,69,83,102,81

%N Permutation of natural numbers: a(1) = 1; a(A001969(1+n)) = A088359(a(n)), a(A000069(1+n)) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.

%H Antti Karttunen, <a href="/A276444/b276444.txt">Table of n, a(n) for n = 1..8191</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(1) = 1, and for n > 1, if A010060(n) = 0 [when n is one of the evil numbers, A001969], a(n) = A088359(a(A245710(n))), otherwise a(n) = A087686(1+a(A115384(n)-1)).

%F As a composition of other permutations:

%F a(n) = A276442(A006068(n)).

%o (Scheme)

%o (definec (A276444 n) (cond ((< n 2) n) ((zero? (A010060 n)) (A088359 (A276444 (A245710 n)))) (else (A087686 (+ 1 (A276444 (- (A115384 n) 1)))))))

%Y Inverse: A276443.

%Y Cf. A000069, A001969, A004001, A010060, A087686, A088359, A115384, A245710.

%Y Similar or related permutations: A006068, A276442, A276446.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Sep 03 2016