A103144 Decimal primes whose decimal representation in hex is also prime.

2, 3, 5, 7, 11, 13, 17, 29, 43, 47, 53, 59, 61, 67, 71, 83, 89, 97, 101, 107, 137, 139, 151, 167, 191, 199, 223, 233, 239, 241, 251, 257, 269, 277, 281, 283, 293, 313, 337, 347, 359, 373, 397, 409, 419, 443, 449, 463, 503, 509, 557, 577, 593, 599, 607, 617, 641

Offset

1,1

Links

Andreas Boe, Table of n, a(n) for n = 1..10000

Example

11 is prime, Hex(11) = 17 is prime, hence 11 is in the sequence.

Mathematica

Select[Prime@ Range@ 120, PrimeQ@ FromDigits[IntegerDigits@ #, 16] &] (* Michael De Vlieger, Nov 05 2018 *)

Prog

(MATLAB) a = primes(300000); j = 0; for i = 1:19000 b = dec2hex(a(i)); c = num2str(b); d = str2num(c); if d < 2^32 if isprime(d) j = j + 1; e(j) = d; end; end; end;
(PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p), 16)); \\ Michel Marcus, Nov 05 2018
(Python)
from sympy import isprime
def ok(n): return isprime(n) and isprime(int(str(n), 16))
print([k for k in range(642) if ok(k)]) # Michael S. Branicky, Dec 04 2022

Crossrefs

Cf. A089971.

Sequence in context: A007693 A174048 A249644 * A105909 A197187 A086498

Adjacent sequences: A103141 A103142 A103143 * A103145 A103146 A103147

Keyword

easy,nonn,base

Author

Lei Zhou, Jan 26 2005

Status

approved