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

1,1

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

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]
Table[Module[{p=2}, While[AnyTrue[{2 Prime[n+1]+p, p Prime[n+1]+2}, CompositeQ], p=NextPrime[p]]; p], {n, 80}] (* Harvey P. Dale, Jul 05 2026 *)

Prog

(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

Crossrefs

Cf. A000040, A065091, A073703, A106067.

Sequence in context: A393422 A198923 A056597 * A019624 A120275 A021656

Adjacent sequences: A329970 A329971 A329972 * A329974 A329975 A329976

Keyword

nonn,changed

Author

Ivan N. Ianakiev, Jun 08 2020

Status

approved