A080794 Numbers k whose digits are all contained, in any order, within the digits of prime(k).

7, 73, 94, 217, 281, 309, 321, 324, 325, 392, 624, 715, 751, 841, 886, 945, 976, 1307, 1384, 1395, 1491, 1492, 1532, 1723, 1785, 1970, 2741, 2845, 2956, 2971, 2977, 3593, 3637, 3673, 3751, 3805, 4153, 4230, 4321, 4345, 4391, 4437, 4759, 4978, 4980, 5174, 5317

Offset: 1

Author

Harvey P. Dale, Mar 13 2003

Keywords

• base
• easy
• nonn

Examples

			6347 is a term because prime(6347) = 63347.
886 is a term because prime(886) = 6883.
11 is not a term because prime(11) = 31, which does not contain two 1's.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Programs

Mathematica

okQ[n_] := Module[{idnp=IntegerDigits[Prime[n]], sidn=Sort[IntegerDigits[n]]}, Intersection[idnp, sidn]==sidn]; Select[Range[10000], okQ]

Python

from sympy import nextprime
from collections import Counter
from itertools import count, islice
def agen2(): # generator of terms
    pk = 2
    for k in count(1):
        cpk, ck = Counter(str(pk)), Counter(str(k))
        if all(cpk[d] >= ck[d] for d in ck): yield (k, pk)
        pk = nextprime(pk)
print(list(islice(agen2(), 47))) # Michael S. Branicky, Sep 10 2022

Extensions

Missing terms inserted by Michael S. Branicky, Sep 10 2022