%I #26 Nov 13 2021 08:34:09

%S 11,13,191,223,251,3019,3023,3037,3067,3259,3323,3517,3533,3547,3581,

%T 3583,4027,4091,4093,48079,48091,48383,48571,48589,49103,49117,52189,

%U 52223,52667,52733,53197,56267,56269,56509,56527,56543,56767,56779,56783,56827,64717,64763,769019,769231,769243,769247,769469,769487

%N Primes whose hexadecimal representation contains only consonants.

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

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

%H Michael S. Branicky, <a href="/A238090/b238090.txt">Table of n, a(n) for n = 1..21472</a> (all terms with <= 9 hexadecimal digits; terms 1..166 from N. J. A. Sloane)

%e The first few terms and their hexadecimal representations (written with least significant "digit" on the left) are:

%e 11, [B]

%e 13, [D]

%e 191, [F, B]

%e 223, [F, D]

%e 251, [B, F]

%e 3019, [B, C, B]

%e 3023, [F, C, B]

%e 3037, [D, D, B]

%e 3067, [B, F, B]

%e 3259, [B, B, C]

%e 3323, [B, F, C]

%e ...

%o (Python)

%o from sympy import isprime, primerange

%o def ok(p): return set(hex(p)[2:]) <= set("bcdf")

%o def aupton(limit): return [p for p in primerange(1, limit+1) if ok(p)]

%o print(aupton(769487)) # _Michael S. Branicky_, Nov 13 2021

%o (Python) # faster version for going to large numbers

%o from sympy import isprime

%o from itertools import product

%o def auptohd(m): # terms up to m hex digits

%o 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)]

%o print(auptohd(7)) # _Michael S. Branicky_, Nov 13 2021

%Y Cf. A140969.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Feb 19 2014, corrected Feb 20 2014