A020467 Primes that contain digits 5 and 7 only.

5, 7, 557, 577, 757, 5557, 7577, 7757, 57557, 75557, 75577, 77557, 555557, 575557, 575777, 577757, 757577, 775757, 775777, 5555777, 5557757, 5575777, 5577577, 5755577, 5775557, 5777557, 7575577, 7577777, 55555777, 55575757, 55755757, 55757777, 57557557

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Crossrefs

Subsequence of A030096, A260827-A260831, and A284380.

Programs

Magma

[p: p in PrimesUpTo(55755757 ) | Set(Intseq(p)) subset [5, 7]];// Vincenzo Librandi, Jul 27 2012

Mathematica

Flatten[Table[Select[FromDigits/@Tuples[{5,7},n],PrimeQ],{n,8}]]

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "57")
    for mp in multiset_permutations(mpstr, digits):
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(33)) # Michael S. Branicky, May 07 2021