A171763 -id:A171763 - cp's OEIS frontend

A171764 Binary expansion of numbers in A171763.

101, 1001, 1011, 10001, 10011, 10101, 10111, 100001, 100011, 100101, 100111, 101001, 101011, 101101, 101111, 1000001, 1000011, 1000101, 1000111, 1001001, 1001011, 1001101, 1001111, 1010001, 1010011, 1010101, 1010111, 1011001, 1011011, 1011101, 1011111, 10000001

Offset: 1

N. J. A. Sloane, Oct 12 2010

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007088, A171763.

bin[n_] := FromDigits[IntegerDigits[n, 2]]; bin /@ Select[Range[3, 130, 2], IntegerDigits[#, 2][[1 ;; 2]] == {1, 0} &] (* Amiram Eldar, Sep 01 2020 *)

a(n) = A007088(A171763(n)). - Amiram Eldar, Sep 01 2020

A171757 Even numbers whose binary expansion begins 10.

Original entry on oeis.org

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

N. J. A. Sloane, Oct 12 2010

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

Cf. A004761, A171758, A171763, A171764.

A subsequence of A004754.

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

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

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

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

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

A171781 Numbers for which the second bit of the binary expansion is equal to the last bit.

Original entry on oeis.org

2, 3, 4, 7, 8, 10, 13, 15, 16, 18, 20, 22, 25, 27, 29, 31, 32, 34, 36, 38, 40, 42, 44, 46, 49, 51, 53, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125

Offset: 1

N. J. A. Sloane, Oct 12 2010

Note that A005843 INTERSECT A171781 = A171757. This is an example of two sequences which both have a limiting density, but whose intersection does not.

			10 is a term since its binary representation is 1010 and both its second and last bits are 0. - _Amiram Eldar_, Sep 01 2020

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005843, A171782, A171757, A171763.

Select[Range[2, 125], (d = IntegerDigits[#, 2])[[2]] == d[[-1]] &] (* Amiram Eldar, Sep 01 2020 *)

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A171764 Binary expansion of numbers in A171763.

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A171757 Even numbers whose binary expansion begins 10.

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A171781 Numbers for which the second bit of the binary expansion is equal to the last bit.

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Mathematica