A326230 Least k > 1 such that k^n is a twin rank (cf. A002822: 6*k^n +- 1 are twin primes).

2, 5, 28, 70, 2, 1820, 110, 1850, 2520, 220, 2023, 9415, 647, 2880, 2562, 3895, 2, 51240, 525, 3750, 147, 2350, 355, 4480, 2588, 3370, 38157, 1185, 1473, 12530, 4338, 1540, 1988, 535, 102, 22606, 13773, 18895, 16373, 2635, 20428, 76300, 23037, 29005, 11078

Offset

1,1

Comments

Dinculescu observes that when k^2 > 1 is a twin rank (i.e., in A002822) then 5 | k (k is divisible by 5), and if k^3 is a twin rank, then 7 | k; cf. A326232 & A326234. It is unknown whether there are other pairs (a, b) such that a | n whenever n^b > 1 is a twin rank. (Of course 2 | b => 5 | a and 3 | b => 7 | a, so we aren't interested in pairs (a, b) which are consequence of this.)

Links

Table of n, a(n) for n=1..45.

A. Dinculescu, On the Numbers that Determine the Distribution of Twin Primes, Surveys in Mathematics and its Applications, 13 (2018), 171-181.

Prog

(PARI) a(n)=for(k=2, oo, ispseudoprime(6*k^n-1)&&ispseudoprime(6*k^n+1)&&return(k))

Crossrefs

Cf. A326231 .. A326236, A002822.

Sequence in context: A025170 A151775 A286879 * A095159 A047132 A364112

Adjacent sequences: A326227 A326228 A326229 * A326231 A326232 A326233

Keyword

nonn

Author

M. F. Hasler and Antonie Dinculescu, Jun 16 2019

Status

approved