login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074203 Odd n such that the number of 1's in the binary representation of n divides 2^n-1. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)

LINKS

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

MAPLE

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

PROG

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

CROSSREFS

Cf. A000120, A007733, A036259, A074202.

Sequence in context: A295708 A232786 A084875 * A045126 A025385 A261640

Adjacent sequences:  A074200 A074201 A074202 * A074204 A074205 A074206

KEYWORD

base,easy,nonn

AUTHOR

Benoit Cloitre, Sep 17 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)