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A091932 Primes that remain prime when their leading digit in binary representation is replaced by 0.

%I A091932 #21 Jul 11 2021 07:21:44
%S A091932 7,11,13,19,23,29,37,43,61,67,71,83,101,107,131,139,151,157,181,199,
%T A091932 211,229,241,263,269,293,317,353,359,383,419,449,467,479,523,541,571,
%U A091932 601,613,619,643,661,691,709,739,751,769,823,829,859,991,1021,1031,1061
%N A091932 Primes that remain prime when their leading digit in binary representation is replaced by 0.
%C A091932 A053645(a(n)) is prime.
%C A091932 Primes p such that p - 2^floor(log_2(p)) is prime - _T. D. Noe_, Apr 08 2011
%H A091932 T. D. Noe, <a href="/A091932/b091932.txt">Table of n, a(n) for n = 1..1000</a>
%F A091932 A118953(A049084(a(n))) = 1; subsequence of A065380. - _Reinhard Zumkeller_, May 07 2006
%e A091932 A000040(12)=37 --> '100101' --> '[1]00101' --> '[0]00101' --> '101' --> 5, therefore 37 is a term.
%t A091932 Select[Prime[Range[100]], PrimeQ[# - 2^Floor[Log[2, #]]] &] (* _T. D. Noe_, Apr 08 2011 *)
%t A091932 Select[Prime[Range[200]],PrimeQ[FromDigits[Rest[ IntegerDigits[ #,2]],2]]&] (* _Harvey P. Dale_, Apr 08 2016 *)
%o A091932 (Python)
%o A091932 from sympy import isprime, primerange
%o A091932 def ok(p): return isprime((1 << (p.bit_length()-1)) ^ p)
%o A091932 def aupto(lim): return [p for p in primerange(1, lim+1) if ok(p)]
%o A091932 print(aupto(1061)) # _Michael S. Branicky_, Jul 11 2021
%Y A091932 Cf. A091931.
%Y A091932 Cf. A118958.
%K A091932 nonn
%O A091932 1,1
%A A091932 _Reinhard Zumkeller_, Feb 14 2004