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A267100 Self-inverse permutation of natural numbers: a(1) = 1, a(A080147(n)) = A080148(n), a(A080148(n)) = A080147(n).

%I A267100 #9 Feb 03 2016 17:02:03
%S A267100 1,3,2,6,7,4,5,10,12,8,13,9,11,16,18,14,21,15,24,25,17,26,29,19,20,22,
%T A267100 30,33,23,27,35,37,28,40,31,42,32,44,45,34,50,36,51,38,39,53,55,57,59,
%U A267100 41,43,60,46,62,47,65,48,66,49,52,68,54,70,71,56,58,74,61,77,63,64,78,79,67,80,82,69,72,73,75,84,76,87,81
%N A267100 Self-inverse permutation of natural numbers: a(1) = 1, a(A080147(n)) = A080148(n), a(A080148(n)) = A080147(n).
%H A267100 Antti Karttunen, <a href="/A267100/b267100.txt">Table of n, a(n) for n = 1..10001</a>
%H A267100 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A267100 a(1) = 1; for n > 1, if prime(n) mod 4 = 1, then a(n) = A080148(A267097(n)), otherwise a(n) = A080147(A267098(n)).
%F A267100 Other identities. For all n >= 1:
%F A267100 a(n) = A000720(A267101(n)).
%o A267100 (Scheme, two variants)
%o A267100 (define (A267100 n) (A000720 (A267101 n)))
%o A267100 (define (A267100 n) (cond ((<= n 1) n) ((= 1 (modulo (A000040 n) 4)) (A080148 (A267097 n))) (else (A080147 (A267098 n)))))
%Y A267100 Cf. A000040, A000720, A080147, A080148, A267101, A267097, A267098, A267099.
%Y A267100 Cf. also A267107 (a more recursed variant).
%K A267100 nonn
%O A267100 1,2
%A A267100 _Antti Karttunen_, Feb 01 2016