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

1,2

Links

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

Example

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.

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

Prog

(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<<k)
print(list(islice(agen(), 63))) # Michael S. Branicky, Apr 28 2024

Crossrefs

Cf. A133457, A272011.

Sequence in context: A102700 A095371 A047481 * A158704 A131854 A005124

Adjacent sequences: A372322 A372323 A372324 * A372326 A372327 A372328

Keyword

nonn,easy,base

Author

David A. Madore, Apr 27 2024

Status

approved