A327581 a(1) is the smallest prime p such that 6*p^2-1 and 6*p^2+1 are twin primes; for n > 1, a(n) is the smallest prime q > a(n-1) such that 6*q^prime(n)-1 and 6*q^prime(n)+1 are twin primes or 0 if no solution exists.

5, 0, 2557, 51137, 52057, 55373, 88867, 95273, 179947, 236653, 993647, 1010467, 1935533, 2031767, 2138803, 2849317, 8031343, 11696563, 11715133, 18125993, 22615493, 26766633, 26801393, 29963077, 39377893, 58282927, 70354657, 98988257, 119772847, 141442493, 145460123

Offset: 1

Author

Pierre CAMI, Sep 17 2019

Keywords

• nonn

Comments

For prime(2) = 3 there is no solution such that 6*q^3-1 and 6*q^3+1 with q prime are twin primes. Because 7 divides 6*p^3-1 when p == 3, 5, 6 mod 7, 7 divides 6*p^3+1 when p == 1, 2, 4 mod 7. Therefore p can only be 7. But then 6*7^3-1 = 11^2*17 and 6*7^3+1 = 29*71 are not prime numbers, so a(2)=0.

Links

• Pierre CAMI, PFGW Script

Programs

PARI

findp(n, pmin) = {my(pmin = nextprime(pmin+1), q); forprime(p=pmin, , if (isprime(q=6*p^prime(n)-1) && isprime(q+2), return(p));); }
lista(nn) = {my(lasta = 2, newa); print1(findp(1, lasta), ", 0"); for (n=3, nn, newa = findp(n, lasta); print1(", ", newa); lasta = newa;); } \\ Michel Marcus, Sep 20 2019