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Least k such that k*12^n +/- 1 are twin primes.
3

%I #9 May 01 2022 13:20:41

%S 4,1,3,19,33,4,165,35,150,35,205,35,63,435,48,4,223,399,388,149,125,

%T 86,335,491,565,876,73,250,85,526,217,139,557,676,488,629,592,1290,

%U 2110,366,140,2461,6198,6476,2033,751,7258,2054,2275,1345,445

%N Least k such that k*12^n +/- 1 are twin primes.

%t Do[ k = 1; While[ ! PrimeQ[ k*12^n + 1 ] || ! PrimeQ[ k*12^n - 1 ], k++ ]; Print[ k ], {n, 0, 50} ]

%t lktpQ[n_]:=Module[{c=12^n,k=1},While[!AllTrue[k*c+{1,-1},PrimeQ],k++];k]; Array[lktpQ,60,0] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 21 2015 *)

%Y Cf. A063983, A064213, A064214, A064215, A064217, A064218, A064220.

%K nonn

%O 0,1

%A _Robert G. Wilson v_, Sep 21 2001

%E Offset corrected by _Georg Fischer_, May 01 2022