%I #21 Feb 11 2024 13:19:02
%S 443,6827,7607,19801,23581,31183,85093,97213,314777,364621,370477,
%T 382813,450011,524287,1077697,1159601,1177073,1215017,1299833,1311749,
%U 1356197,1458253,1547069,1589123,1613987,1649299,1716619,1851271,1893607,2092799,4404833,4454369,4671857
%N Nonpalindromic primes whose binary expansion, interpreted as a base-10 number, yields a palindromic prime.
%e 443 is a nonpalindromic prime. Its binary expansion is 110111011, which, when interpreted as a base-10 number, is a palindromic prime.
%t Select[Range[5000000], PrimeQ[#] && ! PalindromeQ[#] && PrimeQ[FromDigits[IntegerDigits[#, 2]]] && PalindromeQ[FromDigits[IntegerDigits[#, 2]]] &]
%t ppQ[p_]:=With[{c=FromDigits[IntegerDigits[p,2],10]},PrimeQ[c]&&PalindromeQ[c]]; Select[Prime[ Range[ 330000]],!PalindromeQ[#]&&ppQ[#]&] (* _Harvey P. Dale_, Feb 11 2024 *)
%o (Python)
%o from sympy import isprime, primerange
%o def ispal(s): return s == s[::-1]
%o def aupto(limit):
%o alst = []
%o for p in primerange(13, limit+1):
%o if not ispal(str(p)):
%o b = bin(p)[2:]
%o if ispal(b) and isprime(int(b)): alst.append(p)
%o return alst
%o print(aupto(5*10**6)) # _Michael S. Branicky_, Jun 13 2021
%Y Cf. A002385, A006995.
%K nonn,base
%O 1,1
%A _Tanya Khovanova_, Jun 13 2021