A271500 -id:A271500 - cp's OEIS frontend

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

N. J. A. Sloane, Apr 16 2016

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

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

Cf. A052008, A271498, A271500.

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)];

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

A271499 Positive numbers n such that the number of 1's in the binary expansion of n is not a power of 2.

Original entry on oeis.org

7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 63, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 95, 97, 98, 100, 103, 104, 107, 109, 110, 111, 112, 115, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, 131, 133, 134, 137, 138, 140

Offset: 1

N. J. A. Sloane, Apr 16 2016

			127 = 1111111_2 has seven 1's, so is a term (this distinguishes the sequence from A235336).

Michel Marcus, Table of n, a(n) for n = 1..10000

Complement of A143071.

Similar to but different from A075930, A235336 and A271500.

Select[Range@ 140, ! IntegerQ@ Log2@ First@ DigitCount[#, 2] &] (* Michael De Vlieger, Apr 16 2016 *)

lista(nn) = {for (n=1, nn, my(nbd = hammingweight(n)); if (!((nbd==1) || (nbd==2) || (ispower(nbd,,&k) && (k==2))), print1(n, ", ")););} \\ Michel Marcus, Apr 16 2016

A271499_list = [n for n in range(1,10**6) if bin(bin(n).count('1')).count('1') != 1] # Chai Wah Wu, Apr 16 2016

cp's OEIS Frontend

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.

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