cp's OEIS Frontend

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.

%I A239021 #18 Apr 10 2025 23:22:56
%S A239021 4,105525,10990,15855,344190,2,74580,11580,165592,3759,204918,12670,
%T A239021 99090,78,3978,11655,8979180,10605,55188,1221,2,23340,4431420,39158,
%U A239021 58464,87318,45420,15780,210,91,289422,19740,186410,1293,137664,747,443730,94920,278278
%N 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.
%e A239021 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.
%o A239021 (Python)
%o A239021 from sympy import isprime
%o A239021 def b(n):
%o A239021   for k in range(10**8):
%o A239021     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):
%o A239021       return k
%o A239021 n = 1
%o A239021 while n < 100:
%o A239021   print(b(n))
%o A239021   n += 1
%Y A239021 Cf. A238847, A238848, A231819, A053989, A035092, A034693.
%K A239021 nonn
%O A239021 1,1
%A A239021 _Derek Orr_, Mar 09 2014