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

Author

Derek Orr, Mar 09 2014

Keywords

• nonn

Examples

			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.
		

Crossrefs

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

Programs

Python

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