A181490 Numbers k such that 3*2^k-1 and 3*2^k+1 are twin primes (A001097).

1, 2, 6, 18

Offset: 1

Author

M. F. Hasler, Oct 30 2010

Keywords

• bref
• hard
• more
• nonn

Comments

Sequences A181491 and A181492 list the corresponding primes.

No more terms below three million. - Charles R Greathouse IV, Mar 14 2011

Intersection of A002235 and A002253. - Jeppe Stig Nielsen, Mar 05 2018

Crossrefs

Cf. A001097, A001359, A002235, A002253, A006512, A014574, A294730.

Programs

GAP

Filtered([1..300],k->IsPrime(3*2^k-1) and IsPrime(3*2^k+1)); # Muniru A Asiru, Mar 11 2018

Maple

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

Mathematica

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 *)
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 *)

PARI

for( k=1,999, ispseudoprime(3<
				

Formula

Equals { k | A007283(k) in A014574 } = { k | A153893(k) in A001359 }.

Extensions

Pari program repaired by Charles R Greathouse IV, Mar 14 2011