A285933 a(n) = smallest k such that (6*k-3)*2^n-1 and (6*k-3)*2^n+1 are twin primes.

1, 1, 2, 3, 14, 1, 2, 10, 8, 3, 17, 28, 62, 8, 58, 20, 64, 1, 12, 75, 14, 6, 197, 41, 128, 63, 14, 65, 8, 58, 114, 98, 63, 45, 124, 36, 72, 516, 28, 45, 43, 183, 2, 25, 142, 68, 249, 30, 324, 155, 188, 200, 334, 56, 87, 178, 98, 110, 22, 25, 24, 70, 2, 271, 17, 498, 412, 750, 877

Offset

1,3

Comments

Conjecture: a(n) is ~ (n*log(2))^2/9 as n increases.

Links

Pierre CAMI, Table of n, a(n) for n = 1..1000

Example

(6*1-3)*2^1-1 = 5, (6*1-3)*2^1+1 = 7; 5 and 7 are twin primes so a(1) = 1.
(6*1-3)*2^2-1 = 11, (6*1-3)*2^2+1 = 13; 11 and 13 are twin primes so a(2) = 1.

Mathematica

Table[k = 1; While[Times @@ Boole@ PrimeQ[(6 k - 3) 2^n + {-1, 1}] < 1, k++]; k, {n, 69}] (* Michael De Vlieger, May 04 2017 *)

Prog

(PARI) a(n) = {my(k=1); while (!isprime((6*k-3)*2^n-1) || !isprime((6*k-3)*2^n+1), k++); k; } \\ Michel Marcus, May 01 2017

Crossrefs

Cf. A285808.

Sequence in context: A253575 A027673 A306039 * A281754 A282119 A287096

Adjacent sequences: A285930 A285931 A285932 * A285934 A285935 A285936

Keyword

nonn

Author

Pierre CAMI, Apr 29 2017

Status

approved