A139706 - OEIS

%I #20 Jun 13 2021 06:04:45

%S 1,2,3,4,6,5,7,8,12,10,13,9,14,11,15,16,24,20,25,18,26,21,27,17,28,22,

%T 29,19,30,23,31,32,48,40,49,36,50,41,51,34,52,42,53,37,54,43,55,33,56,

%U 44,57,38,58,45,59,35,60,46,61,39,62,47,63,64,96,80,97,72,98,81,99,68

%N Take n in binary. Rotate the binary digits to the right until a 1 once again appears as the leftmost digit. Convert back into decimal for a(n).

%C This sequence written in binary is A139707.

%C This is a permutation of the positive integers. A139708 is the inverse permutation.

%C Moreover, the first 2^n terms are a permutation of the first 2^n positive integers. Fixed points of the permutation are A272919. - _Ivan Neretin_, May 10 2016

%H Ivan Neretin, <a href="/A139706/b139706.txt">Table of n, a(n) for n = 1..8192</a>

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

%p A139706 := proc(n) local a; a := ListTools[Rotate](convert(n,base,2),1) ; while op(-1,a) = 0 do a := ListTools[Rotate](a,1) ; od: add(op(i,a)*2^(i-1),i=1..nops(a)) : end: seq(A139706(n),n=1..100) ; # _R. J. Mathar_, May 04 2008

%t Table[FromDigits[RotateRight[IntegerDigits[n, 2], IntegerExponent[n, 2] + 1], 2], {n, 72}] (* _Ivan Neretin_, May 10 2016 *)

%Y Cf. A139707 (in binary), A139708 (inverse), A272919 (fixed points).

%K nonn,base,easy

%O 1,2

%A _Leroy Quet_, Apr 30 2008

%E More terms from _R. J. Mathar_, May 04 2008