cp's OEIS Frontend

A053642 Rotate n one binary digit to the left, drop leading zeros, then rotate one binary digit to the right.

%I A053642 #31 Jan 16 2024 08:31:24
%S A053642 1,1,3,1,3,6,7,1,3,6,7,12,13,14,15,1,3,6,7,12,13,14,15,24,25,26,27,28,
%T A053642 29,30,31,1,3,6,7,12,13,14,15,24,25,26,27,28,29,30,31,48,49,50,51,52,
%U A053642 53,54,55,56,57,58,59,60,61,62,63,1
%N A053642 Rotate n one binary digit to the left, drop leading zeros, then rotate one binary digit to the right.
%C A053642 Sequence contains ever-longer copies of A004760. - _Ralf Stephan_, Sep 16 2003
%H A053642 Paolo Xausa, <a href="/A053642/b053642.txt">Table of n, a(n) for n = 1..10000</a>
%F A053642 a(n) = A038572(A006257(n)).
%F A053642 a(n) = n if 3*2^(k-1) <= n < 2^(k+1);
%F A053642 a(n) = a(n - 2^(k-1)) if 2^k <= n < 3*2^(k-1).
%F A053642 a(2n) = 2a(n) - [a(n)==1], a(2n+1) = 2a(n) + 1. - _Ralf Stephan_, Sep 16 2003
%e A053642 a(22)=14 because starting with 10110 the left rotation produces 01101 written as 1101 (i.e., 13) and the right rotation produces 1110 (i.e., 14).
%t A053642 rtt[f_, n_] := FromDigits[f[IntegerDigits[n, 2]], 2];
%t A053642 Array[rtt[RotateRight, rtt[RotateLeft, #]]&, 100] (* _Paolo Xausa_, Jan 16 2024 *)
%o A053642 (PARI) a(n) = n-=1<<logint(n,2); n + 1<<if(n,logint(n,2)+1); \\ _Kevin Ryde_, Jan 13 2024
%Y A053642 Cf. A004760, A006257, A038572.
%Y A053642 Cf. A053641 (right then left).
%K A053642 nonn,base,easy
%O A053642 1,3
%A A053642 _Henry Bottomley_, Mar 22 2000