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

1,1

Comments

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

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A096169 A225526 A090670 * A075794 A192864 A135832

Adjacent sequences: A074829 A074830 A074831 * A074833 A074834 A074835

Keyword

base,easy,nonn

Author

Robert G. Wilson v, Sep 09 2002

Status

approved