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A181490
Numbers k such that 3*2^k-1 and 3*2^k+1 are twin primes (A001097).
9
OFFSET
1,2
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
FORMULA
Equals { k | A007283(k) in A014574 } = { k | A153893(k) in A001359 }.
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 *)
PROG
(PARI) for( k=1, 999, ispseudoprime(3<<k-1)||next; ispseudoprime(3<<k+1)&print(k))
(GAP) Filtered([1..300], k->IsPrime(3*2^k-1) and IsPrime(3*2^k+1)); # Muniru A Asiru, Mar 11 2018
KEYWORD
bref,hard,more,nonn
AUTHOR
M. F. Hasler, Oct 30 2010
EXTENSIONS
Pari program repaired by Charles R Greathouse IV, Mar 14 2011
STATUS
approved