cp's OEIS Frontend

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

%I A071407 #22 Aug 25 2025 09:21:30
%S A071407 2,2,6,6,18,24,6,12,6,12,42,54,30,24,6,120,18,258,24,18,84,132,54,48,
%T A071407 114,42,6,6,48,24,144,30,6,12,12,78,24,36,30,54,132,18,90,36,66,18,42,
%U A071407 30,120,30,36,42,18,18,54,84,60,12,210,12,6,60,150,102,6,210,30,24,6
%N A071407 Least k such that k*prime(n) + 1 and k*prime(n) - 1 are twin primes.
%C A071407 Note that 6 divides a(n) for n > 2. - _T. D. Noe_, Jan 07 2013
%H A071407 T. D. Noe, <a href="/A071407/b071407.txt">Table of n, a(n) for n = 1..10000</a>
%F A071407 From _Amiram Eldar_, Aug 25 2025: (Start)
%F A071407 a(n) = A090530(n) / prime(n).
%F A071407 a(n) = 6 * A294731(n) for n >= 3. (End)
%e A071407 n=4: prime(4)=7, a(4)=6 because 6*prime(4)=42 and {41,43} are primes.
%t A071407 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}]
%o A071407 (Haskell)
%o A071407 a071407 n = head [k | k <- [2,4..], let x = k * a000040 n,
%o A071407                       a010051' (x - 1) == 1, a010051' (x + 1) == 1]
%o A071407 -- _Reinhard Zumkeller_, Feb 14 2013
%Y A071407 Cf. A071256, A071404-A071406, A060256, A060210, A090530, A294731.
%Y A071407 Cf. A071558 (k at every integer).
%Y A071407 Cf. A220141, A220142 (record values).
%K A071407 nonn,changed
%O A071407 1,1
%A A071407 _Labos Elemer_, May 24 2002