A158695 Table T(n,3) read by rows with T(n,1)=a,T(n,2)=b,T(n,3)=c and ((a*M(n))^3)*((a*M(n))^3+b)+c is prime for the least a with least b and c = -1 or 1 and M(n) = n-th Mersenne prime.

1, -1, -1, 1, 1, -1, 1, -1, -1, 3, -1, 1, 10, 1, -1, 2, 1, -1, 8, -1, -1, 15, 1, 1, 4, 1, -1, 90, 1, 1, 72, 1, -1, 33, 1, -1, 114, 1, -1, 15, 1, 1, 37, -1, -1, 516, 1, 1, 301, 1, -1, 2029, -1, -1, 54, 1, -1, 23, -1, -1, 4756, -1, -1, 65, 1, 1, 696, 1, -1, 8503, -1, -1, 3693, 1, 1

Offset

1,10

Comments

All primes certified.

For M(26), a(26)=4166, b(26)=1, c(26)=1.

For M(27), a(27)=5880, b(27)=-1, c(27)=-1.

For M(28), a(28)=3997, b(28)=-1, c(28)=-1; with the following expression being a certified prime ((3997*(2^86243-1))^3)*((3997*(2^86243-1))^3-1)-1.

Links

Table of n, a(n) for n=1..75.

Example

((1*(2^2-1))^3)*((1*(2^2-1))^3-1)-1=701 prime 2^2-1=M(1) a(1)=1 b(1)=-1 c(1)=-1
((1*(2^3-1))^3)*((1*(2^3-1))^3+1)-1=117991 prime 2^3-1=M(2) a(2)=1 b(2)=1 c(2)=-1
((1*(2^5-1))^3)*((1*(2^5-1))^3-1)-1=887473889 prime 2^5-1=M(3) a(3)=1 b(3)=-1 c(3)=-1

Crossrefs

Sequence in context: A267197 A267401 A267338 * A267392 A267553 A268115

Adjacent sequences: A158692 A158693 A158694 * A158696 A158697 A158698

Keyword

sign,tabf

Author

Pierre CAMI, Mar 24 2009

Status

approved