A110559 Least j such that j*n^2 -1 and j*n^2 +1 are twin primes.

4, 1, 2, 12, 6, 2, 18, 3, 10, 6, 12, 3, 12, 18, 18, 57, 12, 5, 120, 12, 2, 3, 132, 2, 42, 3, 58, 45, 12, 7, 72, 15, 10, 3, 6, 2, 60, 30, 12, 3, 168, 2, 192, 18, 2, 33, 48, 10, 138, 39, 8, 63, 42, 22, 60, 42, 32, 3, 120, 6, 90, 18, 40, 165, 204, 7, 90, 18, 70, 6, 72, 27, 30, 15, 6, 18

Offset: 1

Author

Pierre CAMI, Sep 12 2005

Keywords

• nonn

Comments

Define Sj=sum of j(n) for n=1 to N. Define Sn=sum of (2*log(n))^2 for n=1 to N. As N increases Sj/Sn tends to 0.6. - Pierre CAMI, Dec 13 2011

Examples

			12*4*4-1=191, 191 and 193 are twin primes so a(4)=12.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A231819.

Programs

PARI

a(n) = my(j=1); while (!(isprime(p=j*n^2-1) && isprime(p+2)), j++); j; \\ Michel Marcus, Sep 17 2019

Extensions

Extended by Ray Chandler, Sep 15 2005