A271497 If n is a multiple of 3 then a(n) = n/3, otherwise a(n) = n'+n'', where n' (resp. n'') is obtained by sorting the bits of the binary expansion of n into increasing (resp. decreasing) order.

0, 2, 3, 1, 5, 9, 2, 14, 9, 3, 15, 21, 4, 21, 21, 5, 17, 27, 6, 35, 27, 7, 35, 45, 8, 35, 35, 9, 35, 45, 10, 62, 33, 11, 51, 63, 12, 63, 63, 13, 51, 63, 14, 75, 63, 15, 75, 93, 16, 63, 63, 17, 63, 75, 18, 93, 63, 19, 75, 93, 20, 93, 93, 21, 65, 99, 22, 119, 99, 23, 119, 135, 24, 119, 119, 25, 119, 135

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Example

11 = 1011_2, so n' = 0111_2 = 7, n'' = 1110_2 = 14, and therefore a(11) = 7+14 = 21.

Maple

A271497:=proc(n) local t1, t2, len; global b;
if n mod (b+1) = 0 then return(n/(b+1)); fi;
t1:=convert(n, base, b); len:=nops(t1);
t2:=sort(t1);
add(t2[i]*(b^(i-1)+b^(len-i)), i=1..len);
end;
b:=2; [seq(A271497(n), n=0..100)];

Prog

(Python)
from __future__ import division
def A271497(n):
    return int(''.join(sorted(bin(n)[2:])), 2) + int(''.join(sorted(bin(n)[2:], reverse=True)), 2) if n % 3 else n//3 # Chai Wah Wu, Apr 16 2016

Crossrefs

Cf. A052008, A271498, A271500.

Sequence in context: A378432 A359795 A224652 * A293287 A236843 A055905

Adjacent sequences: A271494 A271495 A271496 * A271498 A271499 A271500

Keyword

nonn,base

Author

N. J. A. Sloane, Apr 16 2016

Status

approved