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

Author

N. J. A. Sloane, Apr 16 2016

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A052008, A271498, A271500.

Programs

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)];

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