A238090 Primes whose hexadecimal representation contains only consonants.

11, 13, 191, 223, 251, 3019, 3023, 3037, 3067, 3259, 3323, 3517, 3533, 3547, 3581, 3583, 4027, 4091, 4093, 48079, 48091, 48383, 48571, 48589, 49103, 49117, 52189, 52223, 52667, 52733, 53197, 56267, 56269, 56509, 56527, 56543, 56767, 56779, 56783, 56827, 64717, 64763, 769019, 769231, 769243, 769247, 769469, 769487

Offset: 1

Author

N. J. A. Sloane, Feb 19 2014, corrected Feb 20 2014

Keywords

• nonn
• base

Comments

Primes whose hexadecimal representation contains only the "digits" B, C, D and F.

There are no primes whose hexadecimal representation contains only the vowels A and E (for these would be even numbers greater than 2).

Examples

			The first few terms and their hexadecimal representations (written with least significant "digit" on the left) are:
11, [B]
13, [D]
191, [F, B]
223, [F, D]
251, [B, F]
3019, [B, C, B]
3023, [F, C, B]
3037, [D, D, B]
3067, [B, F, B]
3259, [B, B, C]
3323, [B, F, C]
...
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..21472 (all terms with <= 9 hexadecimal digits; terms 1..166 from N. J. A. Sloane)

Crossrefs

Cf. A140969.

Programs

Python

from sympy import isprime, primerange
def ok(p): return set(hex(p)[2:]) <= set("bcdf")
def aupton(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupton(769487)) # Michael S. Branicky, Nov 13 2021

Python

# faster version for going to large numbers
from sympy import isprime
from itertools import product
def auptohd(m): # terms up to m hex digits
  return [t for t in (int("".join(p), 16) for d in range(1, m+1) for p in product("bcdf", repeat=d)) if isprime(t)]
print(auptohd(7)) # Michael S. Branicky, Nov 13 2021