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A093324
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a(n) is the smallest natural number m such that n^m + m is prime.
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6
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2, 1, 1, 2, 1, 7954, 1, 34, 101, 2, 1, 1181716, 1, 54, 17, 2, 1, 1080, 1, 57910, 9, 2, 1, 202, 2075, 5538, 3
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OFFSET
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0,1
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COMMENTS
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a(n)=1 iff n+1 is prime. For n>1 n+a(n) is odd (for n>1 a(n) is odd iff n is even). a(11) is greater than 7000. a(m) for m = 12, 13, 14, 15, 16, 17 and 18 are 1, 54, 17, 2, 1, 1080, 1. 5^7954 + 7954 is a 5560-digit probable prime.
a(11) is greater than 20165, so every prime of the form 11^m + m has more than 21000 digits. - Farideh Firoozbakht, Jun 10 2004
a(11) is greater than 80000. - T. D. Noe, Mar 07 2007
a(11) is greater than 190000. - T. D. Noe, Jul 31 2008
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LINKS
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EXAMPLE
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a(3)=2 because 3^2 + 2 is prime and 3^1 + 1 is composite.
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MATHEMATICA
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a[n_]:= (For[m=1, !PrimeQ[n^m+m], m++]; m); Do[Print[a[n]], {n, 0, 10}]
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PROG
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(Python)
from sympy import isprime
def a(n):
m = 0
while not isprime(n**m + m): m += 1
return m
for n in range(11):
(Magma)
t:=0;
while not IsPrime(n^t + t) do
t+:=1;
end while;
return t;
end function;
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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