A253549 Maximal prime written in decimal among the base-k representations of the n-th prime, read in base 16, for k=2,3,...,16.

2, 17, 257, 19, 19, 19, 65537, 37, 65809, 53, 307, 257, 53, 547, 563, 293, 101, 277, 4099, 577, 4129, 8737, 787, 137, 577, 257, 593, 4643, 4657, 773, 577, 821, 311, 313, 268501249, 74017, 74257, 8707, 359, 8753, 8963, 613, 9011, 12289, 285212929, 577, 135697

Offset: 1

Author

Chai Wah Wu, Jan 03 2015

Keywords

• nonn
• base

Comments

A base 16 variant of A236174.

Examples

			For n = 19, 67 is the 19th prime, and written in base 2, ..., is '1000011', '2111', '1003', '232', '151', '124', '103', '74', '67', '61', '57', '52', '4b', '47', '43'.  Out of these, when read in as hexadecimal numbers, the first prime is 1003_16 which is 4099_10.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A236174.

Programs

Python

from sympy import prime, isprime
def A253549(n):
    p = prime(n)
    for b in range(2,17):
        x, y, z = p, 0, 1
        while x >= b:
            x, r = divmod(x,b)
            y += r*z
            z *= 16
        y += x*z
        if isprime(y):
            return y