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A266235 Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x^2 + 1.

%I A266235 #13 May 10 2021 02:36:05
%S A266235 5,101,677,28901,3422501,4884101,260176901,4784488901,5887492901,
%T A266235 7370222501,12898144901,14498568101,24840912101,38514062501,
%U A266235 47563248101,56249608901,64014060101,110842384901,123657722501,135755402501,205145584901,279343960901,288680544101
%N A266235 Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x^2 + 1.
%C A266235 For p>2, f(x) is applied an even number of times, twice at least.
%e A266235 a(2) = f(f(3)) = (3^2 + 1)^2 + 1 = 101.
%e A266235 a(3) = f(f(5)) = (5^2 + 1)^2 + 1 = 677.
%t A266235 Take[Union@ Flatten[Table[Nest[#^2 + 1 &, Prime@ n, #], {n, 150}] & /@ Range@ 6] /. n_ /; CompositeQ@ n -> Nothing, 23] (* _Michael De Vlieger_, Jan 06 2016 *)
%o A266235 (Python)
%o A266235 from sympy import isprime
%o A266235 a=[]
%o A266235 TOP=1000000
%o A266235 for p in range(TOP):
%o A266235     if isprime(p):
%o A266235         q=p
%o A266235         while q<TOP:
%o A266235             q = q*q+1
%o A266235             if isprime(q):
%o A266235                 a.append(q)
%o A266235 print(sorted(set(a)))
%Y A266235 Cf. A000040, A266233.
%K A266235 nonn
%O A266235 1,1
%A A266235 _Alex Ratushnyak_, Dec 25 2015