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%I #15 Mar 03 2024 11:35:44
%S 0,0,0,2,2,2,3,3,5,5,3,4,7,4,7,8,11,5,6,9,4,7,12,14,8,11,7,13,10,12,9,
%T 15,15,12,19,9,8,8,20,19,24,11,16,11,18,15,9,13,21,14,24,27,11,26,24,
%U 26,32,13,12,21,14,28,19,27,14,26,14,14,29,24,26,39
%N Given n-th prime p, a(n)=number of primes of the form p+q+1 where q is any prime < p.
%C Conjecture: a(n)>0 for all n>3. - _Dmitry Kamenetsky_, Feb 09 2017
%H Zak Seidov, <a href="/A224908/b224908.txt">Table of n, a(n) for n = 1..1000</a>
%e For n=5, p=11, there are a(5)=2 solutions from 11+5+1=17 and 11+7+1=19.
%t Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p + Prime[i] + 1], c = c + 1]; i++]; c, {n, 72}]
%t Table[p = Prime[n] + 1; Sum[If[PrimeQ[p + Prime[i]], 1, 0], {i, 1, n - 1}], {n, 72}] (* _Zak Seidov_, Apr 19 2013 *)
%t Table[Count[Prime[n]+Prime[Range[n-1]]+1,_?PrimeQ],{n,80}] (* _Harvey P. Dale_, Mar 03 2024 *)
%o (PARI) for(n = 1,72, q = prime (n) + 1; print1 (sum (i = 1, n - 1, isprime (q + prime (i))) ","))\\ _Zak Seidov_, Apr 19 2013
%Y Cf. A210481, A224748.
%K nonn
%O 1,4
%A _Jayanta Basu_, Apr 19 2013
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