A253149 Primes >= 256 that remain primes when the digits are reversed in base 256.

257, 269, 293, 311, 313, 347, 379, 397, 419, 449, 479, 491, 773, 809, 823, 827, 829, 857, 883, 887, 947, 953, 971, 977, 1013, 1283, 1289, 1297, 1301, 1307, 1321, 1327, 1367, 1373, 1399, 1409, 1429, 1439, 1451, 1453, 1481, 1483, 1511, 1523, 1801, 1811, 1847, 1867

Offset: 1

Author

Chai Wah Wu, Dec 30 2014

Keywords

• nonn
• base

Comments

Reversing the digits in base 256 is equivalent to reading a number in big-endian format using little-endian order with 8-bit words. See also A238853.

Examples

			1299647 is prime and written in base 16 is 13 d4 bf whereas bf d4 13 = 12571667 is also prime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..7110
• Wikipedia, Endianness

Crossrefs

Cf. A253147, A253148, A238853.

Programs

Python

from sympy import prime, isprime
def reversedigits(n, b=10): # reverse digits of n in base b
    x, y = n, 0
    while x >= b:
        x, r = divmod(x, b)
        y = b*y + r
    return b*y + x
A253149_list = []
for n in range(1, 300):
    p = prime(n)
    if p > 255 and isprime(reversedigits(p,256)):
        A253149_list.append(p)
print(A253149_list)