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

Author

T. D. Noe, Mar 06 2008

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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}]