A125251 a(n)=sqrt(A051779(n+2)-1)/30.

5, 6, 8, 9, 14, 19, 43, 44, 77, 85, 91, 112, 113, 142, 155, 195, 196, 212, 226, 300, 308, 321, 351, 363, 399, 456, 461, 467, 485, 541, 555, 602, 604, 618, 638, 646, 720, 728, 779, 789, 891, 896, 923, 980, 1009, 1099, 1105, 1150, 1176, 1234, 1253, 1287, 1392

Offset: 1

Author

Zak Seidov, Nov 26 2006

Keywords

• nonn

Comments

Consider twin primes p, q = p + 2 such that pq + 2 is prime. It would seem that there are infinitely many such p. Except for p = 3 and p = 5 all such p appear to be of the form 30k - 1 and the values of k give the current sequence. - James R. Buddenhagen, Jan 09 2007

This is true. Prime numbers (other than 2,3,5) are 30k + 1,7,11,13,17,19,23,29. p+2 is then prime only for p = 30k + 11,17,29; then p(p+2)+2 is 30k + 25,25,1 respectively, so the last case mod 30 is the only one possible. - Gareth McCaughan, Jan 09 2007

This is the sequence of positive integers k such that p = 30*k - 1, q = 30*k + 1 and p*q + 2 are all prime. - James R. Buddenhagen, Jan 09 2007

Examples

			a(1)=5 because A051779(3)=22501 and sqrt(22501-1)/30=5,
a(2)=6 because A051779(4)=32401 and sqrt(32401-1)/30=6.
		

Links

• Zak Seidov, Table of n, a(n) for n=1..2000

Crossrefs

Cf. A051779.

Programs

PARI

isok(n) = isprime(p = 30*n+1) && isprime(q = 30*n-1) && isprime(p*q+2); \\ Michel Marcus, Oct 11 2013