A235982 -id:A235982 - cp's OEIS frontend

A235053 Numbers k of the form p^2 + 1 (for prime p) where k^2 + 1 is also prime.

10, 26, 170, 1850, 2210, 16130, 69170, 76730, 85850, 113570, 120410, 157610, 196250, 218090, 237170, 253010, 332930, 351650, 368450, 452930, 528530, 537290, 597530, 734450, 786770, 822650, 1329410, 2036330, 2211170

Offset: 1

Derek Orr, Jan 03 2014

nonn

Except for 26, all numbers are divisible by 10 and the tens digit is an odd number.

			351650 = 593^2 + 1 (593 is prime) and 351650^2 + 1 is prime, so 351650 is a member of this sequence.

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Numbers in both A066872 and A005574.

Cf. A235982, A235983.

import sympy
from sympy import isprime
{print(n**2+1) for n in range(10**7) if isprime(n) if isprime((n**2+1)**2+1)}

A236069 Primes p such that f(f(p)) is prime where f(x) = x^4 + 1.

Original entry on oeis.org

3, 79, 83, 107, 211, 401, 491, 881, 1013, 1061, 1367, 1637, 1669, 1811, 2029, 2309, 2399, 2459, 2671, 2713, 2963, 3109, 3203, 3407, 3593, 3709, 3733, 3929, 4219, 4457, 4513, 4639, 4703, 4729, 5417, 5641, 6047, 6113

Offset: 1

Michel Marcus and Derek Orr, Jan 19 2014

nonn

			881 is prime and (881^4+1)^4+1 is also prime. So, 881 is a member of this sequence.

Cf. A235982.

isok(p) = isprime(p) && (q = p^4+1) && isprime(q^4+1); \\ Michel Marcus, Jan 19 2014

import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p) and isprime((p**4+1)**4+1)}

a(n) = (A235982(n)-1)^(1/4).

cp's OEIS Frontend

A235053 Numbers k of the form p^2 + 1 (for prime p) where k^2 + 1 is also prime.

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