cp's OEIS Frontend

A292349 Pri-most primes: primes p such that the majority of bits in the binary representation of p satisfy the following: complementing this bit produces a prime number.

%I A292349 #23 Oct 06 2024 09:44:51
%S A292349 7,19,23,43,71,101
%N A292349 Pri-most primes: primes p such that the majority of bits in the binary representation of p satisfy the following: complementing this bit produces a prime number.
%C A292349 Primes in A292348.
%C A292349 Conjecture: the sequence is finite.
%C A292349 Any further terms are > 10^12. - _Lucas A. Brown_, Oct 05 2024
%t A292349 Select[Prime@ Range[10^5], Function[n, Function[d, 2 Count[Array[FromDigits[#, 2] &@ MapAt[Mod[# + 1, 2] &, d, #] &, Length@ d], _?PrimeQ] > Length@ d]@ IntegerDigits[n, 2]]] (* _Michael De Vlieger_, Dec 08 2017 *)
%o A292349 (Python)
%o A292349 from sympy import isprime, primerange
%o A292349 for i in primerange(1, 1000):
%o A292349   delta = 0
%o A292349   bit = 1
%o A292349   while  bit <= i:
%o A292349     if isprime(i^bit): delta += 1
%o A292349     else:              delta -= 1
%o A292349     bit*=2
%o A292349   if delta > 0:  print(str(i), end=',')
%Y A292349 Cf. A000040, A137985, A292348.
%K A292349 nonn,base,more,hard
%O A292349 1,1
%A A292349 _Alex Ratushnyak_, Dec 07 2017