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

1,1

Comments

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

Links

Table of n, a(n) for n=1..23.

Example

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

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 *)

Prog

(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)))

Crossrefs

Cf. A000040, A266233.

Sequence in context: A081220 A210362 A041187 * A266452 A354332 A074790

Adjacent sequences: A266232 A266233 A266234 * A266236 A266237 A266238

Keyword

nonn

Author

Alex Ratushnyak, Dec 25 2015

Status

approved