A281316 Prime number p such that the decimal representation of its binary reflected Gray code is also a prime.

2, 3, 5, 13, 29, 41, 53, 73, 113, 149, 157, 173, 181, 197, 229, 233, 241, 293, 313, 317, 349, 373, 397, 541, 557, 653, 661, 673, 733, 757, 769, 773, 797, 809, 857, 953, 977, 1009, 1033, 1109, 1181, 1193, 1217, 1277, 1289, 1301, 1433, 1549, 1637, 1709, 1733, 1741, 1877, 1993, 2029, 2053, 2081

Offset: 1

Author

Indranil Ghosh, Jan 20 2017

Keywords

• nonn
• base

Comments

Prime number p such that A003188(p) is in A000040.

Examples

			53 is in the sequence because the decimal representation of its binary reflected Gray code is 47 and both 53 and 47 are primes.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A003188, A281227.

Programs

Maple

q:= n-> andmap(isprime, [n, Bits[Xor](n, iquo(n, 2))]):
select(q, [$2..3500])[];  # Alois P. Heinz, Jan 08 2025

Python

from sympy import isprime
def G(n):
    return int(bin(n^(n//2))[2:], 2)
i=1
j=1
while j<=10000:
    if  isprime(i)==True and isprime(G(i))==True:
        print(f"{j} {i}")
        j+=1
    i+=1