A239020 Smallest number k such that k*n +/- 1 and k*n^2 +/- 1 are two sets of twin primes. a(n) = 0 if no such number exists.

4, 3, 2, 15, 6, 2, 150, 75, 20, 6, 78, 85, 2490, 30, 18, 195, 5160, 490, 330, 12, 2, 870, 330, 13, 42, 105, 2280, 375, 12, 41, 1632, 720, 90, 3, 216, 2, 1380, 615, 98, 84, 438, 65, 600, 210, 148, 735, 3870, 115, 138, 39, 182, 2715, 16590, 48, 60, 63, 210, 120

Offset

1,1

Comments

If n>3 is odd and not a multiple of 3, then a(n) is a multiple of 6; e.g., a(5) = 6, a(7) = 150, a(11) = 78. If n>3 is even and not a multiple of 3, then a(n) is a multiple of 3. In short, for n>1, k*n should be a multiple of 6. - Zak Seidov, Mar 13 2014

Links

Table of n, a(n) for n=1..58.

Example

1*2 +/- 1 (1 and 3) and 1*2^2 +/- 1 (3 and 5) are not two sets of twin primes. 2*2 +/- 1 (3 and 5) and 2*2^2 +/- 1 (7 and 9) are not two sets of twin primes. However, 3*2 +/- 1 (5 and 7) and 3*2^2 +/- 1 (11 and 13) are two sets of twin primes. Thus, a(2) = 3.

Prog

(Python)
from sympy import isprime
def b(n):
  for k in range(10**5):
    if isprime(k*n+1) and isprime(k*n-1) and isprime(k*(n**2)+1) and isprime(k*(n**2)-1):
      return k
n = 1
while n < 100:
  print(b(n))
  n += 1
(PARI) a(n) = {k = 1; while (! (isprime(k*n+1) && isprime(k*n-1) && isprime(k*n^2+1) && isprime(k*n^2-1)), k++); k; } \\ Michel Marcus, Mar 15 2014

Crossrefs

Cf. A231819, A053989, A035092, A034693.

Sequence in context: A274601 A202696 A319541 * A293211 A330778 A061312

Adjacent sequences: A239017 A239018 A239019 * A239021 A239022 A239023

Keyword

nonn

Author

Derek Orr, Mar 09 2014

Status

approved