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.

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

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 * A369519 A213623 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