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

1,1

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.

Links

Table of n, a(n) for n=1..56.

Prog

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

Crossrefs

Cf. A002110, A005235, A037153.

Sequence in context: A135246 A109543 A229168 * A091567 A241896 A076186

Adjacent sequences: A248711 A248712 A248713 * A248715 A248716 A248717

Keyword

nonn

Author

Werner D. Sand, Oct 12 2014

Status

approved