A202996 Least prime q such that prime(n)^2 - q^2 - 1 and prime(n)^2 - q^2 + 1 are twin primes or 0 if no solution.

0, 0, 0, 0, 7, 0, 7, 7, 17, 23, 19, 7, 19, 19, 11, 11, 11, 7, 19, 37, 7, 19, 23, 19, 13, 31, 29, 17, 7, 23, 29, 23, 59, 113, 19, 23, 31, 151, 19, 7, 23, 37, 73, 7, 19, 19, 41, 19, 7, 31, 53, 41, 17, 43, 11, 17, 59, 73, 19, 173, 23, 47, 19, 53, 11, 31, 19, 23

Offset

1,5

Comments

Conjecture: a(n) > 0 for n > 6.

Conjecture: With Sq=sum of q for n=1 to N and Sp=sum of p(n) for n=1 to N, lim sup Sq/Sp = 0.

Links

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

Example

No solution for n=1 to 4 prime(n) = 2, 3, 5, 7.
For prime(5)=11, 11^2-7^2-1 = 71, 71 and 73 twin primes so q(5)=7.
No solution for prime(6)=13
For prime(7)=17, 17^2-7^2-1=239, 239 and 241 twin primes so q(7)=7.

Prog

(PARI) a(n)=my(p=prime(n)); forprime(q=2, p-1, if(isprime(p^2-q^2-1)&&isprime(p^2-q^2+1), return(q))); 0 \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Sequence in context: A011438 A321022 A216185 * A019597 A096444 A246918

Adjacent sequences: A202993 A202994 A202995 * A202997 A202998 A202999

Keyword

nonn

Author

Pierre CAMI, Dec 27 2011

Status

approved