

A118967


If n doesn't occur among the first (n1) terms of the sequence, then a(n) = 2n. If n occurs among the first (n1) terms of the sequence, then a(n) = n/2.


2



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, 54, 56, 58, 15, 62, 64, 66, 17, 70, 72, 74, 19, 78, 20, 82, 21, 86, 88, 90, 23, 94, 96, 98, 25, 102, 104, 106, 27, 110, 28, 114, 29, 118, 120, 122, 31, 126, 32, 130, 33, 134, 136
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OFFSET

1,2


COMMENTS

Sequence is a permutation of the positive integers. It also is its own inverse (i.e. a(a(n)) = n).
From Carl R. White, Aug 23 2010: (Start)
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.
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)


LINKS

Table of n, a(n) for n=1..68.


FORMULA

From Carl R. White, Aug 23 2010: (Start)
a(1) = 1;
a(2^m) = 2^(m(1)^m), m > 0;
a(k*2^m) = k*2^(m+(1)^m), m > 0, odd k > 1. (End)


EXAMPLE

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


MATHEMATICA

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 *)


PROG

(Other) /* 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 */


CROSSREFS

Cf. A118966.
Matches A073675 for all nonpowersoftwo.  Carl R. White, Aug 23 2010
Sequence in context: A282028 A251561 A159193 * A256508 A059030 A066984
Adjacent sequences: A118964 A118965 A118966 * A118968 A118969 A118970


KEYWORD

easy,nonn


AUTHOR

Leroy Quet, May 07 2006


EXTENSIONS

More terms from Robert G. Wilson v, May 16 2006


STATUS

approved



