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

Author

Tanya Khovanova, Sep 09 2022

Keywords

• nonn
• base

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.

Examples

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

Crossrefs

Cf. A171102, A080794.

Programs

Mathematica

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

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