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A277911 Self-inverse permutation of natural numbers induced when A118306 is restricted to A007310.

%I A277911 #12 Nov 07 2016 09:12:37
%S A277911 1,3,2,5,4,7,6,10,17,8,13,26,11,15,14,18,9,16,31,21,20,40,24,23,27,12,
%T A277911 25,30,45,28,19,54,34,33,36,35,38,37,68,22,57,115,44,43,29,47,46,74,
%U A277911 73,51,50,87,55,32,53,58,41,56,180,61,60,96,83,65,64,67,66,39,101,100,75,110,49,48,71,77,76,80,124,78,84,283,63,81,126,88,52
%N A277911 Self-inverse permutation of natural numbers induced when A118306 is restricted to A007310.
%H A277911 Antti Karttunen, <a href="/A277911/b277911.txt">Table of n, a(n) for n = 1..10001</a>
%H A277911 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A277911 a(n) = A126760(A118306(A007310(n))).
%o A277911 (PARI)
%o A277911 A118306(n) = { if(1==n, 1, my(f = factor(n)); my(d = (-1)^primepi(f[1, 1])); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-d)); factorback(f)); };
%o A277911 A007310(n) = n\2*6-(-1)^n; \\ From _M. F. Hasler_, Oct 31 2014
%o A277911 A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From _M. F. Hasler_, Jan 19 2016
%o A277911 A277911(n) = A126760(A118306(A007310(n)));
%o A277911 for(n=1, 10001, write("b277911.txt", n, " ", A277911(n)));
%o A277911 (Scheme) (define (A277911 n) (A126760 (A118306 (A007310 n))))
%Y A277911 Cf. A007310, A118306, A126760.
%Y A277911 Cf. A277908, A277909, A277910 (for "almost fixed points"), also A277907.
%K A277911 nonn
%O A277911 1,2
%A A277911 _Antti Karttunen_, Nov 05 2016