A384449 Primes having only {0, 4, 7} as digits.

7, 47, 4007, 4447, 7477, 44777, 47407, 47777, 74047, 74077, 74707, 74747, 77047, 77447, 77477, 77747, 407047, 407707, 407747, 440047, 444007, 444047, 470077, 470447, 474077, 474707, 477047, 477077, 704447, 704477, 704747, 704777, 707407, 707747, 740477, 744077, 744407, 744707, 747407, 770047

Offset: 1

Author

Jason Bard, May 29 2025

Keywords

• nonn
• base

Links

• Jason Bard, Table of n, a(n) for n = 1..10000
• Index to entries for primes with digits in a given set

Crossrefs

Subsequence of A030432.

Supersequence of A020465.

Cf. Primes that contain only the digits (0,k,7): A199327 (k=1), A261267 (k=2), A260378 (k=3), this sequence (k=4), A260827 (k=5), A261181 (k=9).

Cf. A000040.

Programs

Magma

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0, 4, 7]];

Mathematica

Select[FromDigits/@Tuples[{0, 4, 7}, 6], PrimeQ]

Python

from sympy import sieve
A384449 = [p for p in sieve.primerange(10**6) if all(n in ['0','4','7'] for n in str(p))] # Jwalin Bhatt,  Jun 02 2025

Python

from itertools import count, islice
from gmpy2 import digits, is_prime
def A384449_gen(): # generator of terms
    for i in count(1):
        if is_prime(m:=int(digits(i,3).replace('1','4').replace('2','7'))):
            yield m
A384449_list = list(islice(A384449_gen(),40)) # Chai Wah Wu, Jun 07 2025