cp's OEIS Frontend

A280314 Relationship of prime numbers to multiples of 6. The value of a(n) = 2 if n*6 has two neighboring primes, a(n) = 1 if only n*6+1 is prime, a(n) = -1 if only n*6-1 is prime, and a(n) = 0 if the neighbors of n*6 are both composite.

%I A280314 #10 Apr 07 2020 22:59:13
%S A280314 2,2,2,-1,2,1,2,-1,-1,2,1,2,1,-1,-1,1,2,2,-1,0,1,-1,2,0,2,1,1,-1,-1,2,
%T A280314 0,2,2,0,1,0,1,2,-1,2,0,-1,-1,-1,2,1,2,0,-1,0,1,2,-1,0,1,1,0,2,-1,-1,
%U A280314 1,1,1,-1,-1,1,-1,1,0,2,0,2,1,-1,-1,1,2,-1,0,-1,1,-1,1,-1,-1,0,2,0,0,1,1
%N A280314 Relationship of prime numbers to multiples of 6. The value of a(n) = 2 if n*6 has two neighboring primes, a(n) = 1 if only n*6+1 is prime, a(n) = -1 if only n*6-1 is prime, and a(n) = 0 if the neighbors of n*6 are both composite.
%C A280314 The number of 2's will decrease and the number of 0's will increase as n increases. If there is any pattern (even a local pattern), then the sequence will generate prime numbers, so I predict the values of the sequence have no pattern.
%e A280314 From _Michael De Vlieger_, Dec 31 2016: (Start)
%e A280314 a(1) = 2 since both 1(6)-1 = 5 and 1(6)+1 = 7 are prime.
%e A280314 a(4) = -1 since only 4(6)-1 = 23 is prime; 4(6)+1 = 25 is divisible by 5.
%e A280314 a(20) = 0 since neither 20(6)-1 = 119 nor 20(6)+1 = 121 are prime.
%e A280314 (End)
%t A280314 Table[If[Times @@ Abs@ # == 1, Total@ Abs@ #, Total@ #] &[{-1, 1} Boole@ Map[PrimeQ, n + {-1, 1}]], {n, 6, 546, 6}] (* _Michael De Vlieger_, Dec 31 2016 *)
%Y A280314 Cf. A024898, A024899, A007528, A002476.
%K A280314 sign
%O A280314 1,1
%A A280314 _Shannon Jacobs_, Dec 31 2016