A260827 Primes having only {0, 5, 7} as digits.

5, 7, 557, 577, 757, 5077, 5507, 5557, 7057, 7507, 7577, 7757, 50077, 50707, 50777, 55057, 57077, 57557, 70507, 75557, 75577, 75707, 77557, 500057, 500777, 505777, 507077, 507557, 507757, 550007, 550577, 550757, 555077, 555557, 555707, 557057, 570077, 575077

Offset: 1

Author

Vincenzo Librandi, Aug 01 2015

Keywords

• nonn
• easy
• base

Links

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

Crossrefs

A020467 is a subsequence.

Cf. Primes that contain only the digits (k,5,7): this sequence (k=0), A260828 (k=1), A214705 (k=2), A087363 (k=3), A217039 (k=4), A260829 (k=6), A260830 (k=8), A260831 (k=9).

Cf. A000040.

Programs

Magma

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0,5,7]];

Mathematica

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {0, 5, 7}]=={} &]

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 "057")
    for mp in multiset_permutations(mpstr, digits):
      if mp[0] == "0": continue
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(38)) # Michael S. Branicky, May 07 2021