A171757 Even numbers whose binary expansion begins 10.

2, 4, 8, 10, 16, 18, 20, 22, 32, 34, 36, 38, 40, 42, 44, 46, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178

Offset: 1

Author

N. J. A. Sloane, Oct 12 2010

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1024 from R. J. Mathar)

Crossrefs

Cf. A004761, A171758, A171763, A171764.

A subsequence of A004754.

Programs

Maple

n := 1 ;
for k from 2 to 4000 by 2 do
    dgs := convert(k,base,2) ;
    if op(-1,dgs) = 1 and op(-2,dgs) = 0 then
        printf("%d %d\n",n,k) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Jan 31 2015

Mathematica

Select[Range[2, 200, 2], IntegerDigits[#, 2][[1 ;; 2]] == {1, 0} &] (* Amiram Eldar, Sep 01 2020 *)

PARI

isok(m) = if (!(m%2), my(b=binary(m)); (b[1]==1) && (b[2]==0)); \\ Michel Marcus, Jun 24 2021

Python

from itertools import count, product, takewhile
def agen(): # generator for sequence
    yield 2
    for digits in count(0):
        for mid in product("01", repeat=digits):
            yield int("10" + "".join(mid) + "0", 2)
def aupto(lim): return list(takewhile(lambda x: x <= lim, agen()))
print(aupto(180)) # Michael S. Branicky, Jun 24 2021

Formula

a(n) = 2*A004761(n+1). - Jon Maiga / Georg Fischer, Jun 24 2021