A269855 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).

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

Offset

0,2

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences generated by sieves

Formula

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)).

As a composition of other permutations:

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

Prog

(Scheme, with memoization-macro definec)
(definec (A269855 n) (cond ((<= n 1) (+ n 1)) ((= 1 (A010060 n)) (A250469 (A269855 (- (A115384 n) 1)))) (else (* 2 (A269855 (A245710 n))))))

Crossrefs

Inverse: A269856.

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

Related or similar permutations: A006068, A252755, A269851.

Sequence in context: A303645 A064364 A332977 * A348356 A209274 A303595

Adjacent sequences: A269852 A269853 A269854 * A269856 A269857 A269858

Keyword

nonn

Author

Antti Karttunen, Mar 07 2016

Status

approved