A239021 Smallest number k such that k*n +/- 1, k*n^2 +/- 1, and k*n^3 +/- 1 are three sets of twin primes. a(n) = 0 if no such number exists.

4, 105525, 10990, 15855, 344190, 2, 74580, 11580, 165592, 3759, 204918, 12670, 99090, 78, 3978, 11655, 8979180, 10605, 55188, 1221, 2, 23340, 4431420, 39158, 58464, 87318, 45420, 15780, 210, 91, 289422, 19740, 186410, 1293, 137664, 747, 443730, 94920, 278278

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Example

1*6 +/- 1 (5 and 7), 1*6^2 +/- 1 (35 and 37), and 1*6^3 +/- 1 (215 and 217) are not three sets of twin primes. However, 2*6 +/- 1 (11 and 13), 2*6^2 +/- 1 (71 and 73), and 2*6^3 +/- 1 (431 and 433) are three sets of twin primes. Thus, a(6) = 2.

Prog

(Python)
import sympy
from sympy import isprime
def b(n):
..for k in range(10**8):
....if isprime(k*n+1) and isprime(k*n-1) and isprime(k*(n**2)+1) and isprime(k*(n**2)-1) and isprime(k*(n**3)+1) and isprime(k*(n**3)-1):
......return k
n = 1
while n < 100:
..print(b(n))
..n += 1

Crossrefs

Cf. A238847, A238848, A231819, A053989, A035092, A034693.

Sequence in context: A339450 A273231 A360760 * A193151 A034209 A260614

Adjacent sequences: A239018 A239019 A239020 * A239022 A239023 A239024

Keyword

nonn

Author

Derek Orr, Mar 09 2014

Status

approved