A260828 Primes having only {1, 5, 7} as digits.

5, 7, 11, 17, 71, 151, 157, 557, 571, 577, 751, 757, 1117, 1151, 1171, 1511, 1571, 1777, 5171, 5557, 5711, 5717, 7151, 7177, 7517, 7577, 7717, 7757, 11117, 11171, 11177, 11551, 11717, 11777, 15511, 15551, 17117, 17551, 51151, 51157, 51511, 51517, 51551, 51577

Offset: 1

Author

Vincenzo Librandi, Aug 02 2015

Keywords

• nonn
• easy
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
• Index to entries for primes with digits in a given set

Crossrefs

Subsequence of A030096. A020453, A020455 and A020467 are subsequences.

Cf. similar sequences listed in A260827.

Cf. A000040.

Programs

Magma

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1,5,7]];

Mathematica

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 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 "157")
    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(44)) # Michael S. Branicky, May 07 2021