A364831 Primes whose digits are prime and in nonincreasing order.

2, 3, 5, 7, 53, 73, 733, 773, 5333, 7333, 7753, 55333, 75533, 75553, 77773, 733333, 755333, 775553, 7553333, 7555333, 7775533, 7777753, 55555333, 55555553, 77755553, 555553333, 755555533, 773333333, 777555553, 777773333, 777775333, 777775553, 777777773

Offset: 1

Author

James C. McMahon, Aug 09 2023

Keywords

• nonn
• base

Comments

Intersection of A028867 and A019546.

The subsequence for primes whose digits are prime and in strictly decreasing order has just six terms: 2 3 5 7 53 73 (see A177061).

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A009996, A019546, A177061, A028867.

Programs

Mathematica

Select[Prime[Range[3100000]], AllTrue[d = IntegerDigits[#], PrimeQ] && GreaterEqual @@ d &]

Python

from itertools import count, islice, chain, combinations_with_replacement
from sympy import isprime
def A364831_gen(): # generator of terms
    yield 2
    yield from chain.from_iterable((sorted(s for d in combinations_with_replacement('753',l) if isprime(s:=int(''.join(d)))) for l in count(1)))
A364831_list = list(islice(A364831_gen(),30)) # Chai Wah Wu, Sep 10 2023