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%I #13 Jan 21 2023 16:46:34
%S 0,4,1,5,2,6,3,7,8,12,9,13,10,14,11,15,16,20,17,21,18,22,19,23,24,28,
%T 25,29,26,30,27,31,32,36,33,37,34,38,35,39,40,44,41,45,42,46,43,47,48,
%U 52,49,53,50,54,51,55,56,60,57,61,58,62,59,63,64,68,65,69,66,70,67,71,72
%N Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate right 1 digit.
%C For n>7: a(n) = 8*floor(n/8) + a(n mod 8);
%C permutation of natural numbers with inverse = A080413: A080413(a(n))=n, a(A080413(n))=n;
%C a(a(n))=A080413(n), A080413(A080413(n))=a(n), a(a(a(n)))=n.
%H Harvey P. Dale, <a href="/A080414/b080414.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e a(2)=a('010')='001'=1; a(3)=a('011')='101'=5; a(4)=a('100')='010'=2; a(5)=a('101')='110'=6;
%e a(20)=a('10'100')='10'010'=18; a(21)=a('10'101')='10'110'=22.
%t r3bd[n_]:=Module[{a,b},{a,b}=Reverse[TakeDrop[IntegerDigits[n,2],-3]];FromDigits[Join[a,RotateRight[b]],2]]; Join[{0,4,1,5},Table[r3bd[n],{n,4,80}]] (* _Harvey P. Dale_, Jul 30 2021 *)
%o (Python)
%o def A080414(n): return ((n&6)>>1)+((n&1)<<2)+(n&-8) # _Chai Wah Wu_, Jan 21 2023
%Y Cf. A007088, A004442, A064429, A080412.
%K nonn,base
%O 0,2
%A _Reinhard Zumkeller_, Feb 17 2003
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