A078348 Primes p such that every decimal digit d in p appears exactly d times.

3313, 3331, 32233, 32323, 33223, 123323, 132233, 223133, 223313, 223331, 231323, 233231, 312233, 321323, 323123, 3344443, 3434443, 3443443, 4434343, 4443433, 14334443, 14443343, 14443433, 31434443, 31443443, 33434441, 33555553

Offset: 1

Author

Carlos Rivera, Nov 22 2002

Keywords

• base
• easy
• fini
• nonn

Comments

The largest term is the prime 99999999988888888777777766666655555444223343.

Examples

			In the prime 3313 the digit "1" appears exactly one time and the digit "3" appears exactly three times.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Primes in A108571.

Programs

Mathematica

ddp[x_]:=Select[FromDigits/@Permutations[Flatten[PadRight[{},#,#]&/@x]], PrimeQ]; Take[Flatten[ddp/@Subsets[Range[5]]]//Sort,40] (* Harvey P. Dale, May 13 2020 *)

Python

from sympy import isprime
from itertools import chain, combinations as C, count, islice
from sympy.utilities.iterables import multiset_permutations as mp
def powerset(s):
    return chain.from_iterable(C(s, r) for r in range(len(s)+1))
def agen():
    sumlst = [[] for i in range(46)]
    for s in powerset(range(1, 10)): sumlst[sum(s)].append(s)
    for numdigits in count(1):
        found = set()
        for t in sumlst[numdigits]:
            diglst = "".join(str(i)*i for i in t)
            for m in mp(diglst, numdigits):
                t = int("".join(m))
                if isprime(t): found.add(t)
        yield from sorted(found)
print(list(islice(agen(), 30))) # Michael S. Branicky, Aug 10 2022