cp's OEIS Frontend

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

%I A329973 #67 Jul 17 2020 22:54:44
%S A329973 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,
%T A329973 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,
%U A329973 59,23,31,257,7,47,31,5,7,11,3,67,3,3,43,23
%N A329973 Smallest prime p such that both 2*prime(n+1)+p and p*prime(n+1)+2 are primes.
%C A329973 a(n)=3 if and only if prime(n+1) is in A106067. - _Robert Israel_, Jul 17 2020
%H A329973 Robert Israel, <a href="/A329973/b329973.txt">Table of n, a(n) for n = 1..10000</a>
%p A329973 f:= proc(n) local pn,p;
%p A329973  pn:= ithprime(n+1);
%p A329973  p:= 1;
%p A329973  do
%p A329973    p:= nextprime(p);
%p A329973    if isprime(2*pn+p) and isprime(p*pn+2) then return p fi
%p A329973  od
%p A329973 end proc:
%p A329973 map(f, [$1..100]); # _Robert Israel_, Jul 17 2020
%t A329973 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]
%o A329973 (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
%Y A329973 Cf. A000040, A065091, A073703, A106067.
%K A329973 nonn
%O A329973 1,1
%A A329973 _Ivan N. Ianakiev_, Jun 08 2020