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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.

%I A253549 #6 May 22 2025 10:21:42
%S A253549 2,17,257,19,19,19,65537,37,65809,53,307,257,53,547,563,293,101,277,
%T A253549 4099,577,4129,8737,787,137,577,257,593,4643,4657,773,577,821,311,313,
%U A253549 268501249,74017,74257,8707,359,8753,8963,613,9011,12289,285212929,577,135697
%N 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.
%C A253549 A base 16 variant of A236174.
%H A253549 Chai Wah Wu, <a href="/A253549/b253549.txt">Table of n, a(n) for n = 1..10000</a>
%e A253549 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.
%o A253549 (Python)
%o A253549 from sympy import prime, isprime
%o A253549 def A253549(n):
%o A253549     p = prime(n)
%o A253549     for b in range(2,17):
%o A253549         x, y, z = p, 0, 1
%o A253549         while x >= b:
%o A253549             x, r = divmod(x,b)
%o A253549             y += r*z
%o A253549             z *= 16
%o A253549         y += x*z
%o A253549         if isprime(y):
%o A253549             return y
%Y A253549 Cf. A236174.
%K A253549 nonn,base
%O A253549 1,1
%A A253549 _Chai Wah Wu_, Jan 03 2015