A090530 Least multiple k of prime(n) such that (k-1,k+1) forms a twin prime pair, or 0 if no such number exists.

4, 6, 30, 42, 198, 312, 102, 228, 138, 348, 1302, 1998, 1230, 1032, 282, 6360, 1062, 15738, 1608, 1278, 6132, 10428, 4482, 4272, 11058, 4242, 618, 642, 5232, 2712, 18288, 3930, 822, 1668, 1788, 11778, 3768, 5868, 5010, 9342, 23628, 3258, 17190

Offset: 1

Author

Amarnath Murthy, Dec 07 2003

Keywords

• nonn
• changed

Comments

a(n) is a multiple of 6*prime(n) for n>2. Conjecture: No term is zero.

Examples

			a(5) = 198 = 11*18, (197,199) forms a twin prime pair.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014574, A071407, A090531, A294731 [a(n)/(6*prime(n))].

Programs

Mathematica

For[n = 1, n < 40, n++, a := Prime[n]; k := 2; While[Not[PrimeQ[k*a + 1] && PrimeQ[k*a - 1]], k += 2]; Print[k*a]] (* Stefan Steinerberger, Feb 17 2006 *)

PARI

a(n) = { my(k = 2, p = prime(n)); while (! (isprime(k*p-1) && isprime(k*p+1)), k++); k*p;} \\ Michel Marcus, Nov 12 2017

Formula

a(n) = prime(n) * A071407(n). - Amiram Eldar, Aug 25 2025

Extensions

More terms from David Wasserman, Dec 21 2005

More terms from Stefan Steinerberger, Feb 17 2006