A260827 Primes that contain only the digits (0, 5, 7).

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

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Mathematica

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

Prog

(Magma) [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [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

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.

Sequence in context: A176960 A114368 A260830 * A020467 A089344 A114363

Adjacent sequences: A260824 A260825 A260826 * A260828 A260829 A260830

Keyword

nonn,easy,base

Author

Vincenzo Librandi, Aug 01 2015

Status

approved