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

%I A103144 #21 Dec 05 2022 04:48:55
%S A103144 2,3,5,7,11,13,17,29,43,47,53,59,61,67,71,83,89,97,101,107,137,139,
%T A103144 151,167,191,199,223,233,239,241,251,257,269,277,281,283,293,313,337,
%U A103144 347,359,373,397,409,419,443,449,463,503,509,557,577,593,599,607,617,641
%N A103144 Decimal primes whose decimal representation in hex is also prime.
%H A103144 Andreas Boe, <a href="/A103144/b103144.txt">Table of n, a(n) for n = 1..10000</a>
%e A103144 11 is prime, Hex(11) = 17 is prime, hence 11 is in the sequence.
%t A103144 Select[Prime@ Range@ 120, PrimeQ@ FromDigits[IntegerDigits@ #, 16] &] (* _Michael De Vlieger_, Nov 05 2018 *)
%o A103144 (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;
%o A103144 (PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p), 16)); \\ _Michel Marcus_, Nov 05 2018
%o A103144 (Python)
%o A103144 from sympy import isprime
%o A103144 def ok(n): return isprime(n) and isprime(int(str(n), 16))
%o A103144 print([k for k in range(642) if ok(k)]) # _Michael S. Branicky_, Dec 04 2022
%Y A103144 Cf. A089971.
%K A103144 easy,nonn,base
%O A103144 1,1
%A A103144 _Lei Zhou_, Jan 26 2005