login
Permutation of natural numbers: a(n) = A255551(A252460(n)).
9

%I #13 Feb 28 2015 14:49:44

%S 1,2,3,4,7,6,9,8,5,10,13,12,15,14,11,16,21,18,25,20,17,22,31,24,19,26,

%T 23,28,33,30,37,32,29,34,39,36,43,38,35,40,49,42,51,44,41,46,63,48,27,

%U 50,47,52,67,54,61,56,53,58,69,60,73,62,59,64,81,66,75,68,65,70,79,72,87,74,71,76,57,78,93,80,77,82,99,84,103,86,83,88,105,90

%N Permutation of natural numbers: a(n) = A255551(A252460(n)).

%C a(n) tells which number in array A255551, constructed from Lucky sieve, is at the same position where n is in array A083221, constructed from the sieve of Eratosthenes. As both arrays have A005843 (even numbers) as their topmost row, this permutation fixes all of them.

%H Antti Karttunen, <a href="/A255553/b255553.txt">Table of n, a(n) for n = 1..6840</a>

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

%F a(n) = A255551(A252460(n)).

%F Other identities:

%F a(2n) = 2n. [Fixes even numbers.]

%F For all n >= 1, a(A083141(n)) = A255550(n).

%F For all n >= 2, a(A000040(n)) = A000959(n).

%F For all n >= 2, a(A001248(n)) = A219178(n).

%o (Scheme) (define (A255553 n) (A255551 (A252460 n)))

%Y Inverse: A255554.

%Y Similar or related permutations: A255407, A255408, A249817, A249818, A252460, A255551.

%Y Cf. A000040, A000959, A001248, A083141, A219178, A255550.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 26 2015