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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A364737 A056221 A046849 * A154667 A376482 A093121

Adjacent sequences: A090527 A090528 A090529 * A090531 A090532 A090533

Keyword

nonn

Author

Amarnath Murthy, Dec 07 2003

Extensions

More terms from David Wasserman, Dec 21 2005

More terms from Stefan Steinerberger, Feb 17 2006

Status

approved