1,2

From Robert Israel, Sep 02 2016: (Start)

Odd k is in the sequence iff (7^k-k)/2 is prime.

If k == 1 (mod 3) then k is in the sequence iff (7^k-k)/3 is prime.

708 is in the sequence but is not necessarily a(7). (End)

a(8) >= 384. - Daniel Suteu, Aug 05 2019

Table of n, a(n) for n=1..7.

1 is in this sequence because 7^1-1 = 2*3 is semiprime.

20 is in this sequence because 7^20-20 = 1511201*52800564781 and these two factors are prime.

Res:= NULL:

for n from 1 to 100 do

F:= ifactors(7^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(7^n-n)=2)

fi;

if flag then Res:= Res, n fi

od:

Res; # Robert Israel, Sep 02 2016

Select[Range[80], PrimeOmega[7^# - #]==2 &]

(MAGMA) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [m: m in [1..80] | IsSemiprime(s) where s is 7^m-m];

Cf. similar sequences listed in A252656.

Sequence in context: A269308 A167306 A061840 * A265401 A276503 A067065

Adjacent sequences: A252657 A252658 A252659 * A252661 A252662 A252663

nonn,more

Vincenzo Librandi, Dec 21 2014

a(6) from Robert Israel, Sep 02 2016

a(7) from Daniel Suteu, Aug 05 2019

approved