A140969 Prime numbers whose hexadecimal representation uses only the digits A,B,C,D,E,F (and not the decimal digits).

11, 13, 173, 191, 223, 239, 251, 2731, 2749, 2767, 2797, 3019, 3023, 3037, 3067, 3259, 3307, 3323, 3499, 3517, 3533, 3547, 3581, 3583, 3803, 3821, 3823, 4013, 4027, 4079, 4091, 4093, 43691, 43711, 43759, 43951, 43963, 43997, 44027, 44029, 44203, 44207

Offset: 1

Author

Gil Broussard, Jul 27 2008

Keywords

• base
• nonn
• changed

Examples

			11=B 13=D 113=AD 131=BB
		

Links

• Charles R Greathouse IV, Nov 16 2009, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A238090.

Programs

Mathematica

Select[Prime@ Range[5000], Min[IntegerDigits[#, 16]] > 9 &] (* James C. McMahon, Jul 15 2025 *)

PARI

mindigit(n,b) = if(nA140969(n) = (isprime(n) && mindigit(n,16) > 9) \\ Michael B. Porter, Dec 01 2009

Python

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    yield from (t for d in count(1) for r in product("ABCDEF", repeat=d-1) for e in "BDF" if isprime(t:=int("".join(r)+e, 16)))
print(list(islice(agen(), 44))) # Michael S. Branicky, Aug 31 2025

Extensions

Edited by N. J. A. Sloane, Nov 15 2009