A260828 Primes that contain only the digits (1, 5, 7).

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

1,1

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)

Mathematica

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 5, 7}] == {} &]

Prog

(Magma) [p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [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

Crossrefs

A020453, A020455 and A020467 are subsequences.

Subsequence of A030096.

Cf. similar sequences listed in A260827.

Cf. A000040.

Sequence in context: A134572 A106954 A027755 * A280651 A089785 A226383

Adjacent sequences: A260825 A260826 A260827 * A260829 A260830 A260831

Keyword

nonn,easy,base

Author

Vincenzo Librandi, Aug 02 2015

Status

approved