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

5, 101, 677, 28901, 3422501, 4884101, 260176901, 4784488901, 5887492901, 7370222501, 12898144901, 14498568101, 24840912101, 38514062501, 47563248101, 56249608901, 64014060101, 110842384901, 123657722501, 135755402501, 205145584901, 279343960901, 288680544101

Offset: 1

Author

Alex Ratushnyak, Dec 25 2015

Keywords

• nonn

Comments

For p>2, f(x) is applied an even number of times, twice at least.

Examples

			a(2) = f(f(3)) = (3^2 + 1)^2 + 1 = 101.
a(3) = f(f(5)) = (5^2 + 1)^2 + 1 = 677.
		

Crossrefs

Cf. A000040, A266233.

Programs

Mathematica

Take[Union@ Flatten[Table[Nest[#^2 + 1 &, Prime@ n, #], {n, 150}] & /@ Range@ 6] /. n_ /; CompositeQ@ n -> Nothing, 23] (* Michael De Vlieger, Jan 06 2016 *)

Python

from sympy import isprime
a=[]
TOP=1000000
for p in range(TOP):
    if isprime(p):
        q=p
        while q