cp's OEIS Frontend

A238090 Primes whose hexadecimal representation contains only consonants.

%I A238090 #26 Nov 13 2021 08:34:09
%S A238090 11,13,191,223,251,3019,3023,3037,3067,3259,3323,3517,3533,3547,3581,
%T A238090 3583,4027,4091,4093,48079,48091,48383,48571,48589,49103,49117,52189,
%U A238090 52223,52667,52733,53197,56267,56269,56509,56527,56543,56767,56779,56783,56827,64717,64763,769019,769231,769243,769247,769469,769487
%N A238090 Primes whose hexadecimal representation contains only consonants.
%C A238090 Primes whose hexadecimal representation contains only the "digits" B, C, D and F.
%C A238090 There are no primes whose hexadecimal representation contains only the vowels A and E (for these would be even numbers greater than 2).
%H A238090 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 A238090 The first few terms and their hexadecimal representations (written with least significant "digit" on the left) are:
%e A238090 11, [B]
%e A238090 13, [D]
%e A238090 191, [F, B]
%e A238090 223, [F, D]
%e A238090 251, [B, F]
%e A238090 3019, [B, C, B]
%e A238090 3023, [F, C, B]
%e A238090 3037, [D, D, B]
%e A238090 3067, [B, F, B]
%e A238090 3259, [B, B, C]
%e A238090 3323, [B, F, C]
%e A238090 ...
%o A238090 (Python)
%o A238090 from sympy import isprime, primerange
%o A238090 def ok(p): return set(hex(p)[2:]) <= set("bcdf")
%o A238090 def aupton(limit): return [p for p in primerange(1, limit+1) if ok(p)]
%o A238090 print(aupton(769487)) # _Michael S. Branicky_, Nov 13 2021
%o A238090 (Python) # faster version for going to large numbers
%o A238090 from sympy import isprime
%o A238090 from itertools import product
%o A238090 def auptohd(m): # terms up to m hex digits
%o A238090   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 A238090 print(auptohd(7)) # _Michael S. Branicky_, Nov 13 2021
%Y A238090 Cf. A140969.
%K A238090 nonn,base
%O A238090 1,1
%A A238090 _N. J. A. Sloane_, Feb 19 2014, corrected Feb 20 2014