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

1,1

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).

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)

Example

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]
...

Prog

(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

Crossrefs

Cf. A140969.

Sequence in context: A144375 A140969 A064759 * A093605 A288304 A155967

Adjacent sequences: A238087 A238088 A238089 * A238091 A238092 A238093

Keyword

nonn,base

Author

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

Status

approved