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

1,1

Comments

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

Links

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

Example

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

Maple

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

Prog

(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

Crossrefs

Cf. A000040, A003188, A281227.

Sequence in context: A089477 A099962 A173718 * A329241 A177502 A072536

Adjacent sequences: A281313 A281314 A281315 * A281317 A281318 A281319

Keyword

nonn,base

Author

Indranil Ghosh, Jan 20 2017

Status

approved