cp's OEIS Frontend

A224962 a(n) = number of primes of the form p*q+(p+q) where p = prime(n) and q is any prime < p.

%I A224962 #21 Jul 18 2019 11:30:18
%S A224962 0,1,2,3,2,3,4,4,4,7,3,5,6,4,7,6,8,4,5,6,2,6,10,11,8,8,5,7,10,8,5,11,
%T A224962 8,9,14,6,6,7,11,11,14,9,12,6,13,9,10,7,16,11,11,22,9,16,17,17,21,9,4,
%U A224962 11,6,21,10,14,13,22,10,12,21,15,20,22,13,11,12
%N A224962 a(n) = number of primes of the form p*q+(p+q) where p = prime(n) and q is any prime < p.
%C A224962 Conjecture: a(n) > 0 for all n > 1. - _Dmitry Kamenetsky_, Jul 18 2019
%H A224962 Alois P. Heinz, <a href="/A224962/b224962.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Dmitry Kamenetsky)
%e A224962 For n=3, p=5, there are a(3)=2 solutions from 5*2+(5+2)=17 and 5*3+(5+3)=23.
%e A224962 For n=4, p=7, there are a(4)=3 solutions in the form of 7*2+(7+2)=23, 7*3+(7+3)=31 and 7*5+(7+5)=47.
%p A224962 a:= n-> (p-> add((q-> `if`(isprime((p+1)*(q+1)-1),
%p A224962        1, 0))(ithprime(j)), j=1..n-1))(ithprime(n)):
%p A224962 seq(a(n), n=1..100);  # _Alois P. Heinz_, Jul 18 2019
%t A224962 Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p*Prime[i] + (p + Prime[i])], c = c + 1]; i++]; c, {n, 75}]
%o A224962 (PARI) a(n) = my(p=prime(n), q); sum(k=1, n-1, q=prime(k); isprime(p*q+(p+q))); \\ _Michel Marcus_, Jul 18 2019
%Y A224962 Cf. A224748, A224908, A224925.
%K A224962 nonn
%O A224962 1,3
%A A224962 _Jayanta Basu_, Apr 21 2013