A138205 Least number k such that n^2+k and n^2+k+2 are the smallest twin primes between squares n^2 and (n+1)^2, or 0 if there is no such k.

0, 1, 2, 1, 4, 5, 10, 7, 0, 1, 16, 5, 10, 1, 2, 13, 22, 23, 0, 19, 20, 37, 40, 23, 16, 0, 0, 25, 16, 0, 58, 7, 2, 0, 4, 5, 58, 7, 0, 7, 16, 23, 22, 13, 2, 13, 28, 5, 0, 49, 56, 7, 0, 53, 94, 31, 2, 7, 46, 71, 46, 7, 32, 31, 4, 65, 28, 13, 26, 31, 58, 47, 88, 1, 14, 73, 0, 5, 28, 49, 8, 37

Offset

1,3

Comments

Checking up to n=10^6, it appears that a(n)=0 for only n=1 and the n in A091592.

Links

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

Example

a(7)=10 because (59,61) is the smallest twin-prime pair between 49 and 64.

Mathematica

Table[n2=n^2; k=1; While[k<2n+1 && !(PrimeQ[n2+k] && PrimeQ[n2+k+2]), k++ ]; If[k==2n+1, 0, k], {n, 10^4}]

Crossrefs

Cf. A091591 (number of twin prime pairs between n^2 and (n+1)^2).

Sequence in context: A125156 A119808 A021470 * A137224 A191830 A155944

Adjacent sequences: A138202 A138203 A138204 * A138206 A138207 A138208

Keyword

nonn

Author

T. D. Noe, Mar 06 2008

Status

approved