A224989 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, 2, 1, 3, 2, 4, 3, 2, 3, 4, 3, 5, 4, 5, 3, 3, 6, 5, 6, 6, 6, 3, 7, 5, 5, 6, 9, 4, 8, 3, 7, 7, 5, 6, 5, 7, 6, 8, 8, 9, 5, 10, 9, 12, 8, 6, 8, 9, 13, 10, 12, 9, 8, 12, 9, 7, 14, 9, 10, 8, 13, 9, 9, 11, 10, 6, 13, 12, 11, 8, 9, 17, 9, 12, 6, 11, 14

Offset

1,5

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 are a(5)=2 solutions 5,7 since 11-5+1=7, 11-5-1=5 and 11-7+1=5, 11-7-1=3.

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, 80}]
Table[Count[Prime[p]-Prime[Range[p-1]], _?(AllTrue[#+{1, -1}, PrimeQ]&)], {p, 80}] (* Harvey P. Dale, Aug 12 2025 *)

Crossrefs

Cf. A224748, A224908, A224979, A224980.

Sequence in context: A322886 A320642 A046823 * A124876 A188901 A171618

Adjacent sequences: A224986 A224987 A224988 * A224990 A224991 A224992

Keyword

nonn

Author

Jayanta Basu, Apr 22 2013

Status

approved