A271498 -id:A271498 - cp's OEIS frontend

A271500 Positions of terms greater than 1 in A271498.

7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 32, 33, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 70, 73, 74, 75, 76, 78, 79, 80, 82, 84, 88, 91, 93, 94, 95, 96, 97, 98, 99, 100, 103, 104, 105, 107, 109, 110, 111, 112, 114, 115, 117, 118, 119

Offset: 1

N. J. A. Sloane, Apr 16 2016

There are several similar sequences in the OEIS, but no exact match. It would be nice to have an independent characterization of these numbers (independent of A271498, that is).

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A271497, A271498.

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.

Original entry on oeis.org

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

cp's OEIS Frontend

A271500 Positions of terms greater than 1 in A271498.

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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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