For the n-th twin primes x±1, the least number k > 1 such that k*x±1 are twin primes.
3, 2, 5, 4, 2, 10, 3, 6, 10, 4, 6, 4, 9, 6, 15, 21, 13, 3, 15, 6, 6, 8, 6, 5, 4, 11, 5, 26, 6, 2, 2, 6, 6, 11, 4, 5, 4, 6, 14, 6, 20, 9, 46, 5, 9, 4, 14, 11, 9, 20, 21, 6, 6, 4, 6, 14, 4, 9, 9, 3, 21, 5, 35, 15, 14, 2, 5, 30, 36, 4, 5, 14, 2, 29, 21, 10, 39, 8
1
See S000312 for the lower twin prime k*x-1.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, MathWorld: Twin Primes
(Mma) tp = Select[Prime[Range[1000]], PrimeQ[# + 2] &]; Table[k = 2; While[! (PrimeQ[k*(n + 1) - 1] && PrimeQ[k*(n + 1) + 1]), k++]; k, {n, tp}]
Cf. A001097 (twin primes), S000312.
nonn
T. D. Noe, Nov 04 2014