A220143 Numbers n that yield a new record for k such that n*k+1 and n*k-1 are twin primes.

1, 5, 8, 11, 13, 31, 37, 53, 61, 433, 1957, 2047, 2603, 4079, 9967, 10789, 76943, 81439, 121763, 206867, 233969, 276349, 495931, 626939, 2055943, 3144937, 3585509, 3810949, 6274823, 8407129, 9299471, 19279903, 35531621, 36426301, 38235389, 71701529, 76384717, 98566373

Offset: 1

Author

T. D. Noe, Jan 08 2013

Keywords

• nonn

Comments

These are numbers at which A071558 reaches a new record. The corresponding values of k are in A220144. Note that these numbers are not all primes.

Crossrefs

Cf. A071558, A220144.

Programs

Mathematica

t = {{1, 4}}; Do[k = 1; While[! (PrimeQ[k*n - 1] && PrimeQ[k*n + 1]), k++]; If[k > t[[-1, 2]], AppendTo[t, {n, k}]], {n, 2, 100000}]; Transpose[t][[1]]

Extensions

More terms from Amiram Eldar, Dec 30 2019