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A255408 Permutation of natural numbers: a(n) = A083221(A255128(n)).

%I A255408 #18 Feb 22 2015 23:30:25
%S A255408 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,25,20,21,22,19,24,23,26,
%T A255408 27,28,29,30,49,32,33,34,35,36,31,38,39,40,37,42,41,44,45,46,43,48,55,
%U A255408 50,51,52,47,54,121,56,57,58,77,60,53,62,63,64,65,66,59,68,69,70,61,72,169,74,75,76,67,78,85,80,81,82,71,84,91,86,87
%N A255408 Permutation of natural numbers: a(n) = A083221(A255128(n)).
%C A255408 a(n) tells which number in array A083221 (the sieve of Eratosthenes) is at the same position where n is in Ludic array A255127. As both arrays have A005843 (even numbers) and A016945 as their two topmost rows, both sequences are among the fixed points of this permutation.
%C A255408 Equally: a(n) tells which number in array A083140 is at the same position where n is in the array A255129, as they are the transposes of above two arrays.
%H A255408 Antti Karttunen, <a href="/A255408/b255408.txt">Table of n, a(n) for n = 1..1024</a>
%H A255408 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A255408 a(n) = A083221(A255128(n)).
%F A255408 Other identities. For all n >= 1:
%F A255408 a(2n) = 2n. [Fixes even numbers.]
%F A255408 a(3n) = 3n. [Fixes multiples of three.]
%F A255408 a(A003309(n)) = A008578(n). [Maps Ludic numbers to noncomposites.]
%e A255408 A255127(3,2) = 19 and A083221(3,2) = 25, thus a(19) = 25.
%e A255408 A255127(8,1) = 23 and A083221(8,1) = 19, thus a(23) = 19.
%e A255408 A255127(9,1) = 25 and A083221(9,1) = 23, thus a(25) = 23.
%o A255408 (Scheme) (define (A255408 n) (A083221 (A255128 n)))
%Y A255408 Inverse: A255407.
%Y A255408 Cf. A003309, A008578, A083221, A255127, A255128.
%Y A255408 Similar permutations: A249817.
%K A255408 nonn
%O A255408 1,2
%A A255408 _Antti Karttunen_, Feb 22 2015