|
|
A208936
|
|
Prime production length of the polynomial P = x^2 + x + prime(n): max { k>0 | P(x) is prime for all x=0,...,k-1 }.
|
|
2
|
|
|
1, 2, 4, 1, 10, 1, 16, 1, 1, 2, 1, 1, 40, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) > 0 by definition, and a(n) > 1 iff n is a twin prime; a(n) would be zero for composite n if "prime(n)" was replaced by n.
Euler's original "prime producing polynomial" was P = x^2 - x + 41; changing the sign increases the prime production length by 1.
|
|
LINKS
|
|
|
MAPLE
|
N:= ithprime(n);
for r from 1 do
if not isprime(r^2+r+N) then return(r) end if
end do
|
|
PROG
|
(PARI) a(n)={n=prime(n); for( x=1, 1e9, isprime(x^2+x+n) | return(x))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|