A123345 Numbers containing all divisors in their binary representation.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 52, 53, 55, 56, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 86, 88, 89, 92, 94, 96, 97, 101, 103, 104, 106, 107, 109, 112, 113, 116, 118

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Mathematica

q[n_] := AllTrue[Divisors[n], StringContainsQ[IntegerString[n, 2], IntegerString[#, 2]] &]; Select[Range[100], q] (* Amiram Eldar, Jun 05 2022 *)

Prog

(Haskell)
import Data.List (unfoldr, isInfixOf)
a123345 n = a123345_list !! (n-1)
a123345_list = filter
  (\x -> all (`isInfixOf` b x) $ map b $ a027750_row x) [1..] where
  b = unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2)
-- Reinhard Zumkeller, Oct 27 2012
(Python)
from sympy import divisors
def ok(n):
    b = bin(n)[2:]
    return n and all(bin(d)[2:] in b for d in divisors(n, generator=True))
print([k for k in range(119) if ok(k)]) # Michael S. Branicky, Jun 05 2022

Crossrefs

Complement of A093642. Different from A093641.

Cf. A000040 (subsequence), A027750, A218388.

Sequence in context: A328369 A207674 A162722 * A093641 A209638 A191844

Adjacent sequences: A123342 A123343 A123344 * A123346 A123347 A123348

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 12 2006

Status

approved