A372325 Numbers whose binary expansion has an even number of 1's among positions listed in this sequence.

0, 2, 5, 7, 8, 10, 13, 15, 16, 18, 21, 23, 24, 26, 29, 31, 33, 35, 36, 38, 41, 43, 44, 46, 49, 51, 52, 54, 57, 59, 60, 62, 64, 66, 69, 71, 72, 74, 77, 79, 80, 82, 85, 87, 88, 90, 93, 95, 97, 99, 100, 102, 105, 107, 108, 110, 113, 115, 116, 118, 121, 123, 124

Offset: 1

Author

David A. Madore, Apr 27 2024

Keywords

• nonn
• easy
• base

Examples

			118 is in the sequence because 118 = 2^6 + 2^5 + 2^4 + 2^2 + 2^1, and an even number of the exponents 6,5,4,2,1 (namely 2,5) are in the sequence.
8192 is not in the sequence because 8192 = 2^13, and 13 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A133457, A272011.

Programs

Maple

R:= 0: RL:= [1]: nextp:= 2: m:= 1: count:= 0:
for i from 1 while count < 100 do
  L:= convert(i,base,2);
  if i = nextp then
    nextp:= 2*nextp;
    if R[1+nops(RL)] = m then RL:= [op(RL),m+1] fi;
    m:= m+1;
  fi;
  if convert(L[RL],`+`)::even
  then R:= R,i; count:= count+1
  fi
od:
R; # Robert Israel, May 28 2024

Python

from itertools import count, islice
def agen():  # generator of terms
    aset = 0 # stored as a bitmask
    for k in count(0):
        if (k&aset).bit_count()%2 == 0:
            yield k
            aset += (1<Michael S. Branicky, Apr 28 2024