A074832 Primes whose binary reversal is also prime.

3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 97, 101, 107, 113, 127, 131, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 251, 257, 263, 269, 277, 283, 307, 313, 331, 337, 349, 353, 359, 373, 383, 409, 421, 431, 433, 443

Offset: 1

Author

Robert G. Wilson v, Sep 09 2002

Keywords

• base
• easy
• nonn

Comments

By definition, all Mersenne primes are in this sequence. - Roderick MacPhee, Apr 18 2015

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• K. S. Brown's Mathpages, Reflective and Cyclic Sets of Primes
• Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, Reversible primes, arXiv:2309.11380 [math.NT], 2023. See p. 3.

Crossrefs

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

Programs

Mathematica

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

Python

from sympy import isprime, prime
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