A224963 Let p = prime(n). a(n) = number of primes q less than p, such that both p+q+1 and p+q-1 are primes.

0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 3, 2, 3, 1, 4, 2, 3, 5, 4, 3, 3, 5, 3, 6, 6, 4, 7, 3, 5, 5, 4, 5, 6, 4, 8, 4, 3, 4, 6, 6, 6, 3, 5, 5, 7, 6, 6, 2, 4, 6, 5, 2, 6, 5, 5, 5, 5, 3, 3, 8, 5, 4, 8, 4, 7, 4, 7, 7, 4, 7, 3, 5, 8, 9, 9, 6, 6, 7

Offset: 1

Author

Jayanta Basu, Apr 21 2013

Keywords

• nonn

Examples

			For n=3, p=5, there are no primes q(<5) such that both 5+q+1 and 5+q-1 are primes and hence a(3)=0. Also for n=5, p=11, there is a(5)=1 solution 7 since 11+7+1=19, 11+7-1=17.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A224748, A224908.

Programs

Mathematica

Table[p = Prime[n]; c = 0; i = 1; While[i < n, p1 = p + Prime[i]; If[PrimeQ[p1 + 1] && PrimeQ[p1 - 1], c = c + 1]; i++]; c, {n, 85}]
pq1[n_]:=Module[{pr1=Prime[Range[n-1]],pr2=Prime[n]},Total[ Table[ If[ AllTrue[pr2+pr1[[k]]+{1,-1},PrimeQ],1,0],{k,Length[pr1]}]]]; Array[ pq1,100] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 20 2020 *)