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Primes whose binary reversal is not prime.
4

%I #25 Jul 28 2021 12:57:10

%S 2,19,59,79,89,103,109,137,139,149,157,179,191,211,239,241,271,281,

%T 293,311,317,347,367,379,389,397,401,419,439,457,467,499,523,541,547,

%U 557,563,569,587,593,607,613,641,647,659,673,719,733,743,751,761,769,787,809,811,829,859,863,877,887,919,929,971,977,983,991,997

%N Primes whose binary reversal is not prime.

%t a = {}; For[n = 1, n <= 1000, n++, If[PrimeQ[n], {d = Reverse[ IntegerDigits[n,2]]; If[!PrimeQ[FromDigits[d,2]], AppendTo[a, n]]}]]; a (* Hasler *)

%t Select[Prime[Range[170]], Not[PrimeQ[FromDigits[Reverse[IntegerDigits[#, 2]], 2]]] &] (* _Alonso del Arte_, Jan 13 2012 *)

%o (PARI) forprime(p=1,1e3,if(!isprime(sum(i=1,#b=binary(p),b[i]<<i)\2),print1(p",")))

%o (PARI) isok(k) = isprime(k) && !isprime(fromdigits(Vecrev(binary(k)), 2)); \\ _Michel Marcus_, Feb 19 2021

%o (Python)

%o from sympy import isprime, primerange

%o def ok(p): return not isprime(int(bin(p)[:1:-1], 2))

%o def aupto(lim): return [p for p in primerange(2, lim+1) if ok(p)]

%o print(aupto(1000)) # _Michael S. Branicky_, Feb 19 2021

%Y Complement of A074832 in A000040.

%Y Cf. A076056, the base 10 equivalent.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jan 13 2012