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A266235
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Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x^2 + 1.
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1
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5, 101, 677, 28901, 3422501, 4884101, 260176901, 4784488901, 5887492901, 7370222501, 12898144901, 14498568101, 24840912101, 38514062501, 47563248101, 56249608901, 64014060101, 110842384901, 123657722501, 135755402501, 205145584901, 279343960901, 288680544101
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OFFSET
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1,1
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COMMENTS
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For p>2, f(x) is applied an even number of times, twice at least.
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LINKS
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EXAMPLE
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a(2) = f(f(3)) = (3^2 + 1)^2 + 1 = 101.
a(3) = f(f(5)) = (5^2 + 1)^2 + 1 = 677.
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MATHEMATICA
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Take[Union@ Flatten[Table[Nest[#^2 + 1 &, Prime@ n, #], {n, 150}] & /@ Range@ 6] /. n_ /; CompositeQ@ n -> Nothing, 23] (* Michael De Vlieger, Jan 06 2016 *)
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PROG
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(Python)
from sympy import isprime
a=[]
TOP=1000000
for p in range(TOP):
if isprime(p):
q=p
while q<TOP:
q = q*q+1
if isprime(q):
a.append(q)
print(sorted(set(a)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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