A356980 Numbers k such that prime(k) can be written using only the digits of k (but they may used multiple times).

137, 187, 321, 917, 1098, 1346, 1347, 1349, 1362, 1367, 1384, 1395, 1528, 1583, 1850, 1859, 1876, 1973, 2415, 2490, 2517, 2631, 2632, 2970, 3417, 3529, 3573, 3575, 3590, 3598, 3751, 3785, 3860, 4301, 4537, 4591, 4639, 4927, 4980, 4983, 5231, 5319, 5342, 5790, 6106, 6107

Offset

1,1

Comments

The digits of k can be reused. In other words, the distinct digits of prime(k) form a subset of the set of the distinct digits of k.

This sequence is infinite as every pandigital number is in this sequence, see A171102.

Links

Table of n, a(n) for n=1..46.

Example

The 137th prime number is 773, which can be written with the digits of 137. Thus 137 is in this sequence.

Mathematica

Select[Range[10000], SubsetQ[Sort[IntegerDigits[#]], Sort[IntegerDigits[Prime[#]]]] &]

Prog

(Python)
from sympy import nextprime
from itertools import count, islice
def agen(): # generator of terms
    pk = 2
    for k in count(1):
        if set(str(pk)) <= set(str(k)): yield k
        pk = nextprime(pk)
print(list(islice(agen(), 46))) # Michael S. Branicky, Sep 09 2022

Crossrefs

Cf. A171102, A080794.

Sequence in context: A179912 A108382 A106280 * A139510 A142651 A214265

Adjacent sequences: A356977 A356978 A356979 * A356981 A356982 A356983

Keyword

nonn,base

Author

Tanya Khovanova, Sep 09 2022

Status

approved