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

1,9

Links

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

Example

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.

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 *)

Crossrefs

Cf. A224748, A224908.

Sequence in context: A163367 A057226 A338260 * A073810 A055255 A057768

Adjacent sequences: A224960 A224961 A224962 * A224964 A224965 A224966

Keyword

nonn

Author

Jayanta Basu, Apr 21 2013

Status

approved