A074202 -id:A074202 - cp's OEIS frontend

A128309 a(n) = 2*A000069(n).

2, 4, 8, 14, 16, 22, 26, 28, 32, 38, 42, 44, 50, 52, 56, 62, 64, 70, 74, 76, 82, 84, 88, 94, 98, 100, 104, 110, 112, 118, 122, 124, 128, 134, 138, 140, 146, 148, 152, 158, 162, 164, 168, 174, 176, 182, 186, 188, 194, 196, 200, 206, 208, 214, 218, 220, 224, 230, 234, 236, 242

Offset: 1

N. J. A. Sloane, May 10 2007

These are the even odious numbers. - Tanya Khovanova, May 15 2007

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Different from A074202.

Intersection of A000069 (odious numbers: odd number of 1's in binary expansion) and A005843 (even numbers).

Select[Range[2,300,2],OddQ[DigitCount[#,2,1]]&] (* Harvey P. Dale, Oct 08 2017 *)

is(n)=n%2==0 && hammingweight(n)%2 \\ Charles R Greathouse IV, Mar 22 2013

a(n)=4*n-if(hammingweight(n-1)%2,4,2) \\ Charles R Greathouse IV, Mar 22 2013

def A128309(n): return ((m:=n-1)<<1)+(m.bit_count()&1^1)<<1 # Chai Wah Wu, Mar 09 2023

a(n) = 4n + O(1). - Charles R Greathouse IV, Mar 22 2013

A074203 Odd numbers k such that the number of 1's in the binary representation of k divides 2^k-1.

Original entry on oeis.org

1, 351, 375, 381, 471, 477, 501, 687, 699, 747, 855, 861, 885, 939, 981, 1119, 1143, 1149, 1239, 1245, 1269, 1311, 1335, 1341, 1359, 1371, 1383, 1389, 1395, 1401, 1431, 1437, 1461, 1479, 1485, 1491, 1497, 1509, 1521, 1623, 1629, 1653, 1707, 1749, 1815

Offset: 1

Benoit Cloitre, Sep 17 2002

Except for 1, terms seem always divisible by 3.
From Robert Israel, Jan 14 2019: (Start)
An odd number k is in the sequence if and only if A000120(k) is in A036259 and k is divisible by A007733(A000120(k)).  In particular, there are infinitely many of these for every member of A036259 except 1.
Thus a(2) to a(28842) have A000120(k)=7 and are divisible by 3, but a(28843) = 12582911 has A000120(12582911) = 23 and is divisible by A007733(23) = 11 but not by 3. (End)

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

Cf. A000120, A007733, A036259, A074202.

filter:= n -> 2 &^ n - 1 mod convert(convert(n,base,2),`+`) = 0:
select(filter, [seq(i,i=1..2000,2)]); # Robert Israel, Jan 13 2019

Join[{1}, Select[Range[3, 2000, 2], PowerMod[2, #, DigitCount[#, 2, 1]] == 1 &]] (* Amiram Eldar, Jun 08 2022 *)

isok(n) = (n % 2) && !((2^n-1) % hammingweight(n)); \\ Michel Marcus, Nov 29 2013

cp's OEIS Frontend

A128309 a(n) = 2*A000069(n).

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A074203 Odd numbers k such that the number of 1's in the binary representation of k divides 2^k-1.

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