A187866 Greatest k such that prime(n)*(prime(n)-k)-1 and prime(n)*(prime(n)-k)+1 are twin primes, k >= 0 and k < prime(n) or -1 if no such k exists.

0, 1, -1, 1, -1, -1, 11, 7, 17, 17, -1, -1, 11, 19, 41, -1, 41, -1, 43, 53, -1, -1, 29, 41, -1, 59, 97, 101, 61, 89, -1, 101, 131, 127, 137, 73, 133, 127, 137, 119, 47, 163, 101, 157, 131

Offset: 1

Author

Pierre CAMI, Mar 14 2011

Keywords

• sign

Comments

Conjectures:

1. There are only 11 primes such that k does not exist: 5, 11, 13, 31, 37, 53, 61, 73, 79, 97, 127 (same as A183563).

2. There are only 20 primes such that k(n) = A187563(n): 2, 3, 7, 17, 19, 23, 41, 47, 59, 89, 103, 149, 167, 173, 179, 191, 277, 353, 433, 727.

3. If prime(n) >= 3 there are always at least 2 pairs of twin primes between prime(n) and prime(n)^2.

Links

• Pierre CAMI, Table of n, a(n) for n = 1..25000

Crossrefs

Cf. A187563.

Programs

Mathematica

a[n_] := (k=Prime[n]-1; While[p = Prime[n]*(Prime[n]-k)-1; k>=0 && !(PrimeQ[p] && PrimeQ[p + 2]), k--]; k); a /@ Range[45] (* Jean-François Alcover, Mar 28 2011 *)