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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

import sympy

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 A061312 A019130

Adjacent sequences:  A239017 A239018 A239019 * A239021 A239022 A239023

KEYWORD

nonn

AUTHOR

Derek Orr, Mar 09 2014

STATUS

approved

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)