A269855 - OEIS

%I #8 Mar 07 2016 12:32:02

%S 1,2,3,4,5,6,8,9,7,10,12,15,16,21,25,18,11,14,20,27,24,33,35,30,32,45,

%T 55,42,49,50,36,51,13,22,28,39,40,57,65,54,48,69,85,66,77,70,60,87,64,

%U 93,115,90,91,110,84,123,121,98,100,147,72,105,125,102,17,26,44,63,56,81,95,78,80,117,145,114,119,130,108,159,96

%N a(0) = 1, a(1) = 2, after which, a(nth_odious_number_larger_than_one(n)) = A250469(a(n)), a(nth_evil_number_larger_than_zero(n)) = 2*a(n).

%C Permutation of natural numbers obtained from the sieve of Eratosthenes, combined with the inverse of Gray code. Note the indexing: Domain starts from 0, range from 1.

%H Antti Karttunen, <a href="/A269855/b269855.txt">Table of n, a(n) for n = 0..8191</a>

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

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(0) = 1, a(1) = 2, for n > 1, if A010060(n) = 1 [when n is one of the odious numbers A000069], a(n) = A250469(a(A115384(n)-1)), otherwise [when n is one of the evil numbers A001969], a(n) = 2*a(A245710(n)).

%F As a composition of other permutations:

%F a(n) = A252755(A006068(n)).

%o (Scheme, with memoization-macro definec)

%o (definec (A269855 n) (cond ((<= n 1) (+ n 1)) ((= 1 (A010060 n)) (A250469 (A269855 (- (A115384 n) 1)))) (else (* 2 (A269855 (A245710 n))))))

%Y Inverse: A269856.

%Y Cf. A000069, A001969, A010060, A115384, A245710, A250469.

%Y Related or similar permutations: A006068, A252755, A269851.

%K nonn

%O 0,2

%A _Antti Karttunen_, Mar 07 2016