

A175381


A positive integer of n is included if all positive integers that, when written in binary, occur as substrings in binary n divide n.


2



1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 24, 32, 36, 40, 48, 64, 72, 80, 96, 128, 136, 144, 160, 192, 256, 272, 288, 320, 384, 512, 528, 544, 576, 640, 768, 1024, 1056, 1088, 1152, 1280, 1536, 2048, 2080, 2112, 2176, 2304, 2560, 3072, 4096, 4160, 4224, 4352, 4608
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OFFSET

1,2


COMMENTS

This is the complement of sequence A175382.
This sequence is infinite (because it contains all powers of 2).
The union of powers of 2 and numbers of the form 2^n + 2^k, where floor(n/2) <= k < n.  Ivan Neretin, Nov 24 2016


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000


EXAMPLE

20 in binary is 10100. The positive integers that, when written in binary, occur as substrings in 10100 are: 1 (1 in binary), 2 (10 in binary), 4 (100 in binary), 5 (101 in binary), 10 (1010 in binary), and 20 (10100 in binary.) Since 1, 2, 4, 5, 10, and 20 each are a divisor of 20, then 20 is in this sequence.


MATHEMATICA

mx = 12; Union[2^Range[0, mx], Flatten@Table[2^n + 2^k, {n, 0, mx}, {k, Quotient[n, 2], n  1}]] (* Ivan Neretin, Nov 24 2016 *)


CROSSREFS

Cf. A175382.
Sequence in context: A200678 A088881 A020697 * A213623 A074715 A216365
Adjacent sequences: A175378 A175379 A175380 * A175382 A175383 A175384


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Apr 24 2010


EXTENSIONS

Spelling corrected by Jason G. Wurtzel, Sep 04 2010
a(11)a(53) from Lars Blomberg, May 05 2011


STATUS

approved



