For the n-th twin primes x±1, the least number k*x-1 such that k*x±1 are twin primes for k > 1.
11, 11, 59, 71, 59, 419, 179, 431, 1019, 431, 827, 599, 1619, 1151, 2969, 4787, 3119, 809, 4229, 1871, 2087, 3359, 2591, 2309, 2087, 6269, 2999, 16067, 3851, 1319, 1619, 4931, 4967, 9437, 3527, 5099, 4127, 6299, 14867, 6551, 23039, 11069, 58787, 6449, 11717
1
See S000313 for the value of k for the n-th twin prime. See S000305 for the chain of twin primes beginning with 3.
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 + 1) - 1, {n, tp}]
Cf. A001097 (twin primes), S000305, S000313.
nonn
T. D. Noe, Nov 04 2014