A103557 Least k such that k*((prime(n)#)^2)-1 and k*((prime(n)#)^2)+1 are twin primes.

1, 2, 7, 6, 6, 104, 152, 116, 181, 6, 78, 89, 85, 262, 133, 57, 77, 35, 237, 140, 315, 397, 663, 48, 1135, 382, 318, 261, 542, 352, 120, 31, 1430, 553, 43, 913, 1235, 122, 1008, 602, 222, 1562, 255, 6293, 1231, 2507, 1029, 1413, 5986, 3860, 45, 2622, 3033, 457

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Example

1*((2*3)^2)-1 = 35 is composite, 2*((2*3)^2)-1 = 71 is prime, 2*((2*3)^2)+1 = 73 is prime twin of 71 so a(2) = 2.

Mathematica

a[n_] := Module[{k = 1, p = Product[Prime[i], {i, 1, n}]}, While[!(PrimeQ[k*p^2-1] && NextPrime[k*p^2-1] == k*p^2+1), k++]; k]; Array[a, 50] (* Amiram Eldar, Jul 17 2021 *)

Crossrefs

Cf. A001097, A002110.

Sequence in context: A127817 A199173 A047232 * A210963 A210965 A189959

Adjacent sequences: A103554 A103555 A103556 * A103558 A103559 A103560

Keyword

nonn

Author

Pierre CAMI, Mar 23 2005

Extensions

More terms from Amiram Eldar, Jul 17 2021

Status

approved