

A238090


Primes whose hexadecimal representation contains only consonants.


2



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
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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



