A173041 -id:A173041 - cp's OEIS frontend

A383749 Positive numbers k whose decimal expansion does not contain the decimal expansion of any proper divisor of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 27, 29, 34, 37, 38, 43, 46, 47, 49, 53, 54, 56, 57, 58, 59, 67, 68, 69, 73, 74, 76, 78, 79, 83, 86, 87, 89, 94, 97, 98, 203, 207, 209, 223, 227, 229, 233, 239, 247, 249, 253, 257, 259, 263, 267, 269, 277, 283, 289, 293, 299, 307

Offset: 1

Rémy Sigrist, May 08 2025

Also fixed points of A121042.
This sequence is infinite as it contains A173041.
a(n) > 5 contains no decimal digit 1 and does not end in 2 or 5. - Michael S. Branicky, May 11 2025

			The proper divisors of 54 are 1, 2, 3, 6, 9, 18 and 27; none of them appear in the decimal expansion of 54 so 54 belongs to this sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A011531, A027751, A038772, A121042, A383592.

A038603 and A173041 are subsequences.

A383749Q[k_] := SelectFirst[Divisors[k], StringContainsQ[IntegerString[k], IntegerString[#]] &] == k;
Select[Range[500], A383749Q] (* Paolo Xausa, May 12 2025 *)

is(n, base = 10) = {
    my (d = digits(n, base));
    for (i = 1, #d,
        if (d[i],
            for (j = i, #d,
                if ((i!=1 || j!=#d) && n % fromdigits(d[i..j], base)==0,
                    return (0);););););
    return (1);}

from itertools import count, islice
from sympy import divisors
def A383749_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:not any(dA383749_list = list(islice(A383749_gen(),40)) # Chai Wah Wu, May 10 2025

def ok(n):
    s = str(n)
    subs = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1) if s[i]!='0')
    return n and not any(n%v == 0 for ss in subs if n > (v:=int(ss)) > 0)
print([k for k in range(308) if ok(k)]) # Michael S. Branicky, May 11 2025

A177134 Primes of the form 2*10^k + 3.

Original entry on oeis.org

5, 23, 2003, 200003, 2000003, 20000003, 2000000000003, 20000000000000003, 200000000000000003, 20000000000000000000003, 2000000000000000000000003, 200000000000000000000000000000000003

Offset: 1

Vincenzo Librandi, Dec 10 2010

nonn

Makoto Kamada, Prime numbers of the form 200...003.

Cf. A081677, A101951, A173041.

[ a: n in [0..250] | IsPrime(a) where a is 2*10^n + 3 ];

a(n) = A173041(A081677(n)).

A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)(210^(A081677(k-1))+3).

Original entry on oeis.org

609, 6660999, 666666609999999, 6666666660999999999, 66666666666666666099999999999999999, 666666666666666666666666609999999999999999999999999, 6666666666666666666666666660999999999999999999999999999

Offset: 1

Felix Fröhlich, Sep 06 2014

For any n there exists a k such that A246880(n)=A002277(k-1)*A173041(k).

Subsequence of A246880.

cp's OEIS Frontend

A383749 Positive numbers k whose decimal expansion does not contain the decimal expansion of any proper divisor of k.

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A177134 Primes of the form 2*10^k + 3.

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Magma

Formula

A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)(210^(A081677(k-1))+3).

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Author

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cp's OEIS Frontend

A383749 Positive numbers k whose decimal expansion does not contain the decimal expansion of any proper divisor of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Python

A177134 Primes of the form 2*10^k + 3.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)*(2*10^(A081677(k-1))+3).

Views

Author

Keywords

Comments

Crossrefs

A246881 a(n)=A246880(n) where no k exists such that A246880(n)=A002277(k)(210^(A081677(k-1))+3).