A329973 Smallest prime p such that both 2*prime(n+1)+p and p*prime(n+1)+2 are primes.

5, 3, 3, 7, 3, 3, 3, 7, 3, 5, 23, 67, 3, 7, 7, 13, 5, 5, 7, 5, 5, 67, 3, 3, 37, 17, 43, 5, 13, 3, 7, 127, 3, 19, 5, 17, 53, 3, 3, 43, 5, 19, 23, 3, 3, 101, 17, 3, 41, 37, 13, 17, 7, 7, 37, 3, 59, 23, 31, 257, 7, 47, 31, 5, 7, 11, 3, 67, 3, 3, 43, 23

Offset: 1

Author

Ivan N. Ianakiev, Jun 08 2020

Keywords

• nonn

Comments

a(n)=3 if and only if prime(n+1) is in A106067. - Robert Israel, Jul 17 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A065091, A073703, A106067.

Programs

Maple

f:= proc(n) local pn,p;
 pn:= ithprime(n+1);
 p:= 1;
 do
   p:= nextprime(p);
   if isprime(2*pn+p) and isprime(p*pn+2) then return p fi
 od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 17 2020

Mathematica

f[n_Integer/;n>1]:=Module[{p=3},While[Or[CompositeQ[2*Prime[n]+p],CompositeQ[p*Prime[n]+2]],p=NextPrime[p]];p];f/@Range[2,100]

PARI

a(n) = my(p=2,q=prime(n+1)); while(!isprime(2*q+p) || !isprime(p*q+2), p=nextprime(p+1)); p; \\ Michel Marcus, Jun 08 2020