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return next(filter(lambda m:isprime(1-m**k+m**(k<<1)), count(2))) # Chai Wah Wu, Oct 22 2024
(Python)
from itertools import count
from sympy import isprime, integer_log
def A205506(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1))
k = bisection(f, n, n)
return next(filter(lambda m:isprime(1-m**k+m**(k<<1)), count(2))) # Chai Wah Wu, Oct 22 2024
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a(n) = A085396is smallest positive m such that Phi(A033845(n),m) is prime. - Chai Wah Wu, Sep 16 2024
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