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.

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, 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, 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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..91.

Example

From Michael De Vlieger, Dec 31 2016: (Start)
a(1) = 2 since both 1(6)-1 = 5 and 1(6)+1 = 7 are prime.
a(4) = -1 since only 4(6)-1 = 23 is prime; 4(6)+1 = 25 is divisible by 5.
a(20) = 0 since neither 20(6)-1 = 119 nor 20(6)+1 = 121 are prime.
(End)

Mathematica

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 *)

Crossrefs

Cf. A024898, A024899, A007528, A002476.

Sequence in context: A168141 A232654 A105971 * A080354 A238529 A195150

Adjacent sequences: A280311 A280312 A280313 * A280315 A280316 A280317

Keyword

sign

Author

Shannon Jacobs, Dec 31 2016

Status

approved