A248714 - OEIS

%I #18 Oct 19 2014 16:21:50

%S 3,5,7,11,17,29,23,41,29,37,89,79,89,71,439,389,163,79,151,73,89,211,

%T 113,113,419,167,139,199,173,137,487,197,401,167,739,641,461,199,223,

%U 331,379,401,293,223,251,647,593,613,317,271,257,947,331,347,593,433

%N a(n) = p - prime(n)#^2, where prime(n)# is the product of the first n primes and p is the smallest prime > prime(n)#^2 + 1.

%C Conjecture: Analogous to Fortune's Conjecture (A005235) all a(n) are prime, so are all members of a(n)=p-k*prime(n)#, k=natural number.

%C Besides, many powers p-prime(n)#^m, m=natural number, behave as well, e.g. p-prime(n)#^29 does, p-prime(n)#^30 does not.

%o (PARI) a(n) = {hp = prod(ip=1, n, prime(ip)); nextprime(hp^2+2) - hp^2;} \\ _Michel Marcus_, Oct 12 2014

%o (MuPAD) q:=1;p:=1;for i from 1 to 100 do q:=nextprime(q+1);p:=p*q;N:=nextprime(p^2+2)-p^2;print(i,N);end_for: \\ _Werner D. Sand_, Oct 13 2014

%Y Cf. A002110, A005235, A037153.

%K nonn

%O 1,1

%A _Werner D. Sand_, Oct 12 2014