A118967 - OEIS

%I #23 May 05 2023 14:14:10

%S 1,4,6,2,10,3,14,16,18,5,22,24,26,7,30,8,34,9,38,40,42,11,46,12,50,13,

%T 54,56,58,15,62,64,66,17,70,72,74,19,78,20,82,21,86,88,90,23,94,96,98,

%U 25,102,104,106,27,110,28,114,29,118,120,122,31,126,32,130,33,134,136

%N If n doesn't occur among the first (n-1) terms of the sequence, then a(n) = 2n. If n occurs among the first (n-1) terms of the sequence, then a(n) = n/2.

%C Sequence is a permutation of the positive integers. It also is its own inverse (i.e. a(a(n)) = n).

%C From _Carl R. White_, Aug 23 2010: (Start)

%C Powers of two with even exponent exchange places with the next lowest power of two with odd exponent and vice versa, i.e., 4 swaps with 2, 256 with 128, etc.

%C For other numbers where n > 1, the even component (the power of two in n's prime factorization) is exchanged the opposite way: A power of two with _odd_ component is exchanged for the next lowest (even exponent) power of two and vice versa. (End)

%F From _Carl R. White_, Aug 23 2010: (Start)

%F a(1) = 1;

%F a(2^m) = 2^(m-(-1)^m), m > 0;

%F a(k*2^m) = k*2^(m+(-1)^m), m > 0, odd k > 1. (End)

%e a(6) = 2^1*3 -> 2^0*3 = 3; a(12) = 2^2*3 -> 2^3*3 = 24; a(25)=2^0*25 -> 2^1*25 = 50; a(1024) = 2^10 -> 2^9 = 512; a(5120) = 2^10*5 -> 2^11*5 = 10240. - _Carl R. White_, Aug 23 2010

%t f[s_] := Block[{n = Length@s}, Append[s, If[ MemberQ[s, n], n/2, 2n]]]; Drop[ Nest[f, {1}, 70], {2}] (* _Robert G. Wilson v_, May 16 2006 *)

%o (bc) /* GNU bc */ scale=0;1;for(n=2;n<=100;n++){m=0;for(k=n;!k%2;m++)k/=2;if(k==1){2^(m-(-1)^m)}else{k*2^(m+(-1)^m)}} /* _Carl R. White_, Aug 23 2010 */

%Y Cf. A118966.

%Y Matches A073675 for all non-powers-of-two. - _Carl R. White_, Aug 23 2010

%K easy,nonn

%O 1,2

%A _Leroy Quet_, May 07 2006

%E More terms from _Robert G. Wilson v_, May 16 2006