A080413 - OEIS

%I #19 May 11 2026 14:09:00

%S 0,2,4,6,1,3,5,7,8,10,12,14,9,11,13,15,16,18,20,22,17,19,21,23,24,26,

%T 28,30,25,27,29,31,32,34,36,38,33,35,37,39,40,42,44,46,41,43,45,47,48,

%U 50,52,54,49,51,53,55,56,58,60,62,57,59,61,63,64,66,68,70,65,67,69,71,72

%N Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate left 1 digit.

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

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).

%F For n>7: a(n) = 8*floor(n/8) + a(n mod 8).

%F A permutation of natural numbers with inverse = A080414: A080414(a(n))=n, a(A080414(n))=n.

%F a(a(n))=A080414(n), A080414(A080414(n))=a(n), a(a(a(n)))=n.

%F From _Elmo R. Oliveira_, May 11 2026: (Start)

%F a(n) = a(n-1) + a(n-8) - a(n-9).

%F G.f.: (2*x*((1+x^4)*(1+x+x^2)) - x^4*(5-x^4)) / ((1+x)*(1+x^2)*(1+x^4)*(x-1)^2). (End)

%e a(2)=a('010')='100'=4; a(3)=a('011')='110'=6; a(4)=a('100')='001'=1; a(5)=a('101')='011'=3;

%e a(20)=a('10'100')='10'001'=17; a(21)=a('10'101')='10'011'=19.

%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 4, 6, 1, 3, 5, 7, 8}, 73] (* _Georg Fischer_, Jul 03 2025 *)

%o (Python)

%o def A080413(n): return ((n&3)<<1)+bool(n&4)+(n&-8) # _Chai Wah Wu_, Jan 21 2023

%Y Cf. A004442, A007088, A064429, A080412, A080414.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Feb 17 2003