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Self-inverse permutation of natural numbers: a(2n) = A003961(A048673(n)), a(2n-1) = 2 * A245448(n).
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%I #12 Jul 29 2014 13:47:05

%S 2,1,4,3,6,5,8,7,10,9,22,27,20,15,14,33,18,17,28,13,34,11,62,29,26,25,

%T 12,19,24,75,68,43,16,21,46,69,118,45,82,243,142,99,32,63,38,35,78,

%U 171,50,49,52,51,116,275,74,147,122,81,60,59,88,23,44,201,66,65,98,31,36

%N Self-inverse permutation of natural numbers: a(2n) = A003961(A048673(n)), a(2n-1) = 2 * A245448(n).

%H Antti Karttunen, <a href="/A243500/b243500.txt">Table of n, a(n) for n = 1..8192</a>

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

%F a(2n) = A003961(A048673(n)), a(2n-1) = 2 * A245448(n).

%F a(2n) = A003961(A048673(n)), a(2n-1) = A243502(A064989(2n-1)).

%F a(2n) = A003961((A003961(n)+1)/2), a(2n-1) = 2 * A064216(A064989(2n-1)).

%o (Scheme, two alternative implementations)

%o (define (A243500 n) (cond ((odd? n) (A243502 (A064989 n))) (else (A003961 (A048673 (/ n 2))))))

%o (define (A243500 n) (if (even? n) (A003961 (A048673 (/ n 2))) (* 2 (A245448 (/ (1+ n) 2)))))

%Y Cf. A003961, A048673, A064989, A243502, A244319, A245448.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jul 18 2014