A202996 - OEIS

%I #11 May 13 2013 01:50:01

%S 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,

%T 29,17,7,23,29,23,59,113,19,23,31,151,19,7,23,37,73,7,19,19,41,19,7,

%U 31,53,41,17,43,11,17,59,73,19,173,23,47,19,53,11,31,19,23

%N 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.

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

%C 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.

%H Pierre CAMI, <a href="/A202996/b202996.txt">Table of n, a(n) for n = 1..10000</a>

%e No solution for n=1 to 4 prime(n) = 2, 3, 5, 7.

%e For prime(5)=11, 11^2-7^2-1 = 71, 71 and 73 twin primes so q(5)=7.

%e No solution for prime(6)=13

%e For prime(7)=17, 17^2-7^2-1=239, 239 and 241 twin primes so q(7)=7.

%o (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

%K nonn

%O 1,5

%A _Pierre CAMI_, Dec 27 2011