A187563 Least k >=0 and k < prime(n) such that prime(n)*(prime(n)-k)-1 and prime(n)*(prime(n)-k)+1 are twin primes or -1 if no such k exists.

0, 1, -1, 1, -1, -1, 11, 7, 17, 11, -1, -1, 11, 13, 41, -1, 41, -1, 1, 11, -1, -1, 17, 41, -1, 23, 97, 11, 7, 47, -1, 59, 71, 1, 137, 31, 97, 67, 137, 119, 47, 43, 101, 7, 101, 91, 43, 13, 11, 31, 137, 71, 49, 41, 137, 47, 11, 61, 67

Offset: 1

Author

Pierre CAMI, Mar 13 2011

Keywords

• sign

Comments

Conjectures: there are only 11 primes (5,11,13,31,37,53,61,73,79,97,127) for which k does not exist and there is always at least a pair of twin primes between prime(n) and prime(n)^2.

Links

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

Programs

Mathematica

Table[k = 0; While[k < Prime[n] && ! (PrimeQ[Prime[n]*(Prime[n] - k) - 1] && PrimeQ[Prime[n]*(Prime[n] - k) + 1]), k++]; If[k == Prime[n], k = -1]; k, {n, 100}]