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%I #37 Jan 21 2024 03:42:12
%S 1,2,6,18
%N Numbers k such that 3*2^k-1 and 3*2^k+1 are twin primes (A001097).
%C Sequences A181491 and A181492 list the corresponding primes.
%C No more terms below three million. - _Charles R Greathouse IV_, Mar 14 2011
%C Intersection of A002235 and A002253. - _Jeppe Stig Nielsen_, Mar 05 2018
%F Equals { k | A007283(k) in A014574 } = { k | A153893(k) in A001359 }.
%p a:=k->`if`(isprime(3*2^k-1) and isprime(3*2^k+1),k,NULL); seq(a(k),k=1..1000); # _Muniru A Asiru_, Mar 11 2018
%t fQ[n_] := PrimeQ[3*2^n - 1] && PrimeQ[3*2^n + 1]; k = 1; lst= {}; While[k < 15001, If[fQ@k, AppendTo[lst, k]; Print@k]; k++ ] (* _Robert G. Wilson v_, Nov 05 2010 *)
%t Select[Range[20],AllTrue[3*2^#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 24 2014 *)
%o (PARI) for( k=1,999, ispseudoprime(3<<k-1)||next; ispseudoprime(3<<k+1)&print(k))
%o (GAP) Filtered([1..300],k->IsPrime(3*2^k-1) and IsPrime(3*2^k+1)); # _Muniru A Asiru_, Mar 11 2018
%Y Cf. A001097, A001359, A002235, A002253, A006512, A014574, A294730.
%K bref,hard,more,nonn
%O 1,2
%A _M. F. Hasler_, Oct 30 2010
%E Pari program repaired by _Charles R Greathouse IV_, Mar 14 2011
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