A074832 - OEIS

%I #26 Sep 29 2023 11:52:08

%S 3,5,7,11,13,17,23,29,31,37,41,43,47,53,61,67,71,73,83,97,101,107,113,

%T 127,131,151,163,167,173,181,193,197,199,223,227,229,233,251,257,263,

%U 269,277,283,307,313,331,337,349,353,359,373,383,409,421,431,433,443

%N Primes whose binary reversal is also prime.

%C By definition, all Mersenne primes are in this sequence. - _Roderick MacPhee_, Apr 18 2015

%H T. D. Noe, <a href="/A074832/b074832.txt">Table of n, a(n) for n=1..10000</a>

%H K. S. Brown's Mathpages, <a href="http://www.mathpages.com/home/kmath362.htm">Reflective and Cyclic Sets of Primes</a>

%H Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, <a href="https://arxiv.org/abs/2309.11380">Reversible primes</a>, arXiv:2309.11380 [math.NT], 2023. See p. 3.

%e 349 = 101011101, reverse the sequence of ones and zeros: 101110101 = 373 which is also prime.

%t Prime[ Select[ Range[100], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 2]], 2]] &]]

%o (C++) for(int p=0; p<100; p++) { int rp = bitrev(p); if(isprime(p) && isprime(rp)) cout << p << " "; }

%o (Python)

%o from sympy import isprime, prime

%o A074832 = [prime(n) for n in range(1,10**6) if isprime(int(bin(prime(n))[:1:-1],2))] # _Chai Wah Wu_, Aug 14 2014

%Y Cf. A007500 (primes whose decimal reversal is also prime).

%K base,easy,nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 09 2002