A089367 Smallest prime p such that np +1 is a prime, or 0 if no such prime exists.

2, 2, 2, 3, 2, 2, 0, 2, 2, 3, 2, 3, 0, 2, 2, 7, 0, 2, 0, 2, 2, 3, 2, 3, 0, 2, 0, 7, 2, 2, 0, 3, 2, 3, 2, 2, 0, 5, 2, 7, 2, 3, 0, 2, 0, 3, 0, 2, 0, 2, 2, 3, 2, 2, 0, 2, 0, 19, 0, 3, 0, 5, 2, 3, 2, 3, 0, 2, 2, 3, 0, 13, 0, 2, 2, 3, 0, 2, 0, 3, 2, 19, 2, 5, 0, 2, 0, 7, 2, 2, 0, 3, 0, 3, 2, 2, 0, 2, 2, 7, 0, 3, 0, 3

Offset

1,1

Comments

a(2n+1) = 0 if 4n+3 is composite. Conjecture: There are no other zeros.

Links

Robert Israel, Table of n, a(n) for n = 1..20000

Maple

for n from 1 to 245 do if(n mod 2 =1 and not isprime(2*n+1)) then a[n]:=0: else i:=1:while(not isprime(n*ithprime(i)+1)) do i:=i+1:od: a[n]:=ithprime(i):fi:od:seq(a[j], j=1..245); # Sascha Kurz, May 09 2004
N:= 1000: # to get a(n) for n <= 2*N
count:= 0:
a:= Vector(2*N):
for i from 1 to 2*N do if isprime(2*i+1) then
  a[i]:= 2;
  if type(i, even) then count:= count+1 fi
fi od:
for p in select(isprime, [$3..N]) while count < N do
  for q in select(isprime, [seq(2*p*i+1, i=1..N)]) do
     n:= (q-1)/p;
     if a[n] = 0 then a[n]:= p;
        count:= count+1;
     fi
   od
od:
A089367:= [seq(a[i], i=1..2*N)]; # Robert Israel, May 26 2014

Crossrefs

Sequence in context: A071137 A333253 A193990 * A130192 A175064 A349956

Adjacent sequences: A089364 A089365 A089366 * A089368 A089369 A089370

Keyword

nonn

Author

Amarnath Murthy, Nov 08 2003

Extensions

More terms from Sascha Kurz, May 09 2004

Status

approved