A069163 Number of symmetric primes between n^2 and (n+2)^2. Two primes are termed symmetric in n^2 to (n+2)^2 if there is a k < 2n such that mid-k and mid+k are both prime, where mid =n(n+2).

0, 1, 2, 2, 1, 2, 2, 1, 2, 4, 1, 2, 3, 1, 5, 3, 1, 4, 4, 3, 5, 3, 2, 4, 4, 1, 4, 4, 2, 5, 4, 0, 6, 2, 3, 4, 4, 2, 4, 8, 0, 3, 4, 2, 5, 4, 4, 5, 5, 3, 7, 5, 3, 5, 7, 2, 4, 6, 3, 7, 7, 5, 6, 6, 5, 5, 7, 5, 6, 8, 1, 3, 8, 3, 11, 6, 1, 10, 5, 2, 5, 8, 5, 5, 7, 5, 4, 6, 2, 8, 7, 4, 13, 7, 5, 9, 7, 4, 9

Offset

1,3

Comments

This relates primes between n^2 and (n+1)^2 to primes between (n+1)^2 and (n+2)^2. It appears that the number of symmetric primes is zero for only n=0,32,41.

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Example

a(5) = 1 because in the range 25 to 49, the primes 29 and 41 are the only primes symmetric about the number 35.

Mathematica

maxN=100; lst={}; For[n=1, n<maxN, n=n+1, mid=n^2+2n; cnt=0; If[EvenQ[mid], k=1, k=2]; While[k<2n, If[PrimeQ[mid-k]&&PrimeQ[mid+k], cnt++; ]; k=k+2]; AppendTo[lst, cnt] ]; lst

Crossrefs

Cf. A014085.

Sequence in context: A361870 A124800 A247349 * A025260 A227156 A123369

Adjacent sequences: A069160 A069161 A069162 * A069164 A069165 A069166

Keyword

easy,nonn

Author

T. D. Noe, Apr 09 2002

Status

approved