1,1

From Robert Israel, Sep 06 2016: (Start)

Even n is in this sequence iff (6^n-n)/2 is prime.

3*k is in this sequence iff (2*6^(3*k-1)-k is prime.

Also contains 275, 278 and 683.

The only other possible member less than 275 is 259. (End)

Table of n, a(n) for n=1..10.

2 is in this sequence because 6^2-2 = 2*17 is semiprime.

10 is in this sequence because 6^10-10 = 2*30233083 and these two factors are prime.

Res:= NULL:

for n from 1 to 100 do

F:= ifactors(6^n-n, easy)[2];

if add(t[2], t=F) >= 3 or (hastype(F, symbol) and add(t[2], t=F) >= 2)

then flag:= false

elif add(t[2], t=F) = 2 and not hastype(F, symbol) then flag:= true

else

flag:= evalb(numtheory:-bigomega(6^n-n)=2)

fi;

if flag then Res:= Res, n fi

od:

Res; # Robert Israel, Sep 06 2016

Select[Range[90], PrimeOmega[6^# - #]== 2&]

(MAGMA) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [m: m in [1..90] | IsSemiprime(s) where s is 6^m-m];

Cf. similar sequences listed in A252656.

Sequence in context: A043859 A043868 A048329 * A004691 A133335 A062925

Adjacent sequences: A252656 A252657 A252658 * A252660 A252661 A252662

nonn,more

Vincenzo Librandi, Dec 21 2014

approved