A248714 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.

3, 5, 7, 11, 17, 29, 23, 41, 29, 37, 89, 79, 89, 71, 439, 389, 163, 79, 151, 73, 89, 211, 113, 113, 419, 167, 139, 199, 173, 137, 487, 197, 401, 167, 739, 641, 461, 199, 223, 331, 379, 401, 293, 223, 251, 647, 593, 613, 317, 271, 257, 947, 331, 347, 593, 433

Offset: 1

Author

Werner D. Sand, Oct 12 2014

Keywords

• nonn

Comments

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.

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.

Crossrefs

Cf. A002110, A005235, A037153.

Programs

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

PARI

a(n) = {hp = prod(ip=1, n, prime(ip)); nextprime(hp^2+2) - hp^2;} \\ Michel Marcus, Oct 12 2014