A071407 Least k such that k*prime(n) + 1 and k*prime(n) - 1 are twin primes.

2, 2, 6, 6, 18, 24, 6, 12, 6, 12, 42, 54, 30, 24, 6, 120, 18, 258, 24, 18, 84, 132, 54, 48, 114, 42, 6, 6, 48, 24, 144, 30, 6, 12, 12, 78, 24, 36, 30, 54, 132, 18, 90, 36, 66, 18, 42, 30, 120, 30, 36, 42, 18, 18, 54, 84, 60, 12, 210, 12, 6, 60, 150, 102, 6, 210, 30, 24, 6

Offset: 1

Author

Labos Elemer, May 24 2002

Keywords

• nonn
• changed

Comments

Note that 6 divides a(n) for n > 2. - T. D. Noe, Jan 07 2013

Examples

			n=4: prime(4)=7, a(4)=6 because 6*prime(4)=42 and {41,43} are primes.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071256, A071404-A071406, A060256, A060210, A090530, A294731.

Cf. A071558 (k at every integer).

Cf. A220141, A220142 (record values).

Programs

Haskell

a071407 n = head [k | k <- [2,4..], let x = k * a000040 n,
                      a010051' (x - 1) == 1, a010051' (x + 1) == 1]
-- Reinhard Zumkeller, Feb 14 2013

Mathematica

Table[fl=1; Do[s=(Prime[j])*k; If[PrimeQ[s-1]&&PrimeQ[s+1]&&Equal[fl, 1], Print[{j, k}]; fl=0], {k, 1, 2*j^2}], {j, 0, 100}]

Formula

From Amiram Eldar, Aug 25 2025: (Start)

a(n) = A090530(n) / prime(n).

a(n) = 6 * A294731(n) for n >= 3. (End)