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A266239
a(n) is the smallest k such that the following are four primes: prime(n)*k-1, prime(n)*k+1, prime(n)*k^2-1, prime(n)*k^2+1. Or -1 if no such k exists.
0
3, 2, 6, 66, 300, 24, 3744, 27000, 6, 1080, 960, 90, 30, 366, 9204, 8154, 1170, 840, 330, 6090, 84, 27720, 324, 90, 186, 4740, 2856, 6, 24270, 936, 5220, 1560, 6, 1500, 510, 120, 930, 3270, 30, 8520, 29700, 1200, 23310, 1056, 3540, 90, 3420, 2370, 9654, 83040, 2610, 9270, 2610
OFFSET
1,1
COMMENTS
Conjecture: a(n)>1.
EXAMPLE
a(1)=3 because the following are four primes: 2*3-1, 2*3+1, 2*9-1, 2*9+1.
PROG
(Python)
from sympy import isprime
TOP=10**9
for p in range(2, 333):
if isprime(p):
failed = True
for x in range(1, TOP):
if isprime(p*x+1) and isprime(p*x-1) and isprime(p*x*x-1) and isprime(p*x*x+1):
print str(x)+', ',
failed = False
break
if failed: print '-1, ',
(PARI) a(n) = {k = 1; p = prime(n); while (! (isprime(p*k-1) && isprime(p*k+1) && isprime(p*k^2-1) && isprime(p*k^2+1)), k++); k; } \\ Michel Marcus, Dec 27 2015
CROSSREFS
Sequence in context: A025240 A137602 A086550 * A018864 A271610 A019951
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Dec 25 2015
STATUS
approved