A238849 Smallest k such that k*n^3 - 1 and k*n^3 + 1 are twin primes.

4, 9, 4, 3, 24, 2, 24, 30, 58, 3, 12, 19, 96, 3, 10, 165, 114, 11, 390, 159, 2, 30, 114, 10, 18, 12, 24, 6, 42, 19, 72, 24, 30, 72, 24, 3, 150, 189, 40, 54, 348, 5, 24, 93, 14, 33, 324, 9, 150, 81, 70, 39, 354, 3, 138, 42, 56, 51, 180, 16, 18, 9

Offset

1,1

Links

Table of n, a(n) for n=1..62.

Example

a(1) = 4 because for k = 1, 1*(1^3) - 1 = 0 and 1*(1^3) + 1 = 2 are not twin primes, for k = 2, 1 and 3 are not twin primes, for k = 3, 2 and 4 are not twin primes, so the smallest k that works is k = 4: 4*(1^3) - 1 = 3 and 4*(1^3) + 1 = 5 are twin primes.

Prog

(Python)
import sympy
from sympy import isprime
def f(n):
..for k in range(1, 10**4):
....if isprime(k*(n**3)-1) and isprime(k*(n**3)+1):
......return k
n = 1
while n < 10**3:
..print(f(n))
..n += 1

Crossrefs

Cf. A071558, A110559.

Sequence in context: A341953 A341767 A281152 * A360697 A197582 A086277

Adjacent sequences: A238846 A238847 A238848 * A238850 A238851 A238852

Keyword

nonn

Author

Derek Orr, Mar 06 2014

Status

approved