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A080544 In binary representation: keep the first digit and rotate right the others twice.

%I A080544 #17 Sep 03 2015 19:00:49
%S A080544 1,2,3,4,5,6,7,8,10,12,14,9,11,13,15,16,20,24,28,17,21,25,29,18,22,26,
%T A080544 30,19,23,27,31,32,40,48,56,33,41,49,57,34,42,50,58,35,43,51,59,36,44,
%U A080544 52,60,37,45,53,61,38,46,54,62,39,47,55,63,64,80,96,112,65,81,97,113,66
%N A080544 In binary representation: keep the first digit and rotate right the others twice.
%C A080544 a(n) = A080542(A080542(n)); permutation of natural numbers with inverse = A080543: A080543(a(n))=a(A080543(n))=n.
%H A080544 Ivan Neretin, <a href="/A080544/b080544.txt">Table of n, a(n) for n = 1..8192</a>
%H A080544 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A080544 a(n) = n - 3*A053645(A002265(n)) + (2^(A000523(n)-2)-1)*A010873(n) for n >= 4. - _Robert Israel_, Sep 01 2015
%e A080544 a(20)=a('10100')='10001'=17; a(25)=a('11001')='10110'=22.
%p A080544 f:= proc(n) local m,a;
%p A080544      m:= ilog2(n);
%p A080544      a:= n mod 4;
%p A080544      (n - a - 2^m)/4 + 2^(m-2)*a+2^m
%p A080544 end proc:
%p A080544 f(2):= 2:
%p A080544 map(f, [$1..100]); # _Robert Israel_, Sep 01 2015
%t A080544 Table[FromDigits[Prepend[RotateRight[Rest[IntegerDigits[n, 2]], 2], 1], 2], {n, 72}] (* _Ivan Neretin_, Aug 30 2015 *)
%K A080544 nonn,base
%O A080544 1,2
%A A080544 _Reinhard Zumkeller_, Feb 20 2003