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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.
1
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
1,1
COMMENTS
A base 16 variant of A236174.
EXAMPLE
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.
PROG
(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
CROSSREFS
Cf. A236174.
Sequence in context: A098622 A020561 A099702 * A002590 A029735 A291206
KEYWORD
nonn,base
AUTHOR
Chai Wah Wu, Jan 03 2015
STATUS
approved